LOUGHBOROUGH UNIVERSITY

PHYSICS DEPARTMENT

Final Year Projects 2012-13 Some projects are marked as suitable for MPhys but others may be adapted in an extended form to MPhys requirements. 1. Title: Chaotic electron transport in semiconductor superlattice Supervisor: Dr K Alekseev Type: Theoretical Prerequisites: Solid State Physics, Mechanics, Commitment to programming is

essential Suitability: BSc or MPhys (suitable for one or two students Semiconductor superlattices (SLs) are nanostructures made from alternating layers

of two different semiconductor materials, usually with very similar lattice constants, for example, GaAs and AlGaAs. Due to the different energy band gaps of the two materials, the conduction band edge of an ideal superlattice is periodically modulated. The current- voltage characteristics of SLs are usually highly nonlinear due to a variety of quantum-mechanical effects, including resonant tunneling, the formation of Wannier-Stark energy level ladders, and the occurrence of Bloch oscillations. The latter makes SL promising for various applications in ultra high-frequency electronics as generators, amplifiers and detectors of electro-magnetic waves. Recent theoretical and experimental work has revealed that the single-particle trajectories of electrons moving through SL in the presence of a tilted magnetic or alternating electric field can demonstrate very complicated chaotic behavior, which can counter-intuitively make a significant improvement of transport characteristics of SL [1-3]. A student will be involved in the theoretical research of chaotic electron dynamics in semiconductors and their nanostructures, and physical phenomena associated with single-electron chaos. A significant part of the project consists in computer simulations based on numerical solutions of a set of ordinary differential equations, hence programming skills are essential. Besides the methods of modeling of electron transport in semiconductor devices, the student will become familiar with different types of oscillations that can occur in nature: periodic, quasiperiodic, and chaotic. This will be a great opportunity to master the basic tools of nonlinear dynamics, including phase trajectory analysis, Poincaré sections, and elements of bifurcation analysis. [1] http://pre.aps.org/abstract/PRE/v77/i2/e026209 [2] http://prl.aps.org/abstract/PRL/v103/i11/e117401 [3]  http://prb.aps.org/abstract/PRB/v80/i20/e205318

2. Title: Amplification of THz radiation in semiconductor nanostructures Supervisor: Dr K Alekseev Type: Theoretical Prerequisites: Solid State Physics, Mechanics, Commitment to programming is

essential Suitability: BSc or MPhys (suitable for one or two students) The recent interest in terahertz (THz) science and technology is strongly stimulated

by their various promising applications (see the department webpage: http://www.lboro.ac.uk/departments/ph/research/THz.html ) There exists a strong demand for miniature, coherent, monochromatic, solid-state, room temperature operating sources and amplifiers of THz radiation. A student will be involved in theoretical research devoted to the development of new principles of amplification and generation of THz radiation in quantum nanodevices [1-3] She/he will become familiar with basic tools of the theory of semiconductor superlattices and modelling based on numerical solutions of ordinary differential equations.

[1] http://prl.aps.org/abstract/PRL/v102/i14/e140405 [2] http://prl.aps.org/abstract/PRL/v103/i11/e117401 [3] http://prb.aps.org/abstract/PRB/v80/i20/e205318

3. Title: Using of sound for generation of Terahertz (THz) radiation in

semiconductor nanostructures. Supervisor: Dr K Alekseev Type: Theoretical Prerequisites: Solid State Physics, Mechanics, Commitment to programming is

essential Suitability: BS or MPhys (suitable for one or two students) The presence of deformation waves propagating through solids and associating with

heat transfer and/or sound can be described in terms of quantum quasi-particles known as “phonons”. These quasi-particles can strongly interact with conducting electrons. For example, the frequency response of semiconductor oscillators and detectors is limited by scattering processes including electron-phonon interactions. Surprisingly, though, phonons can serve as a powerful tool for enhancing the electronic and optical properties of solid state devices. E.g., in “SASER” [1], recently developed acoustic analogous to the laser, the amplification of coherent sound waves now opens the new and effective way to control electron transport in nanostructures like semiconductor superlattice. The student will be involved in the cutting-edge theoretical research on using phonon waves for generation and control of very high-frequency (THz) electron transport in semiconductor nanostructures. The student will become familiar with basic analytical and numerical tools of the theory of semiconductors, of modeling of solid state electronic devices, and of the theory of oscillations and waves. [1] http://prl.aps.org/abstract/PRL/v96/i21/e215504

4. Title: Synchronization of noise-induced oscillations. Supervisor: Dr A Balanov Type: Theoretical Prerequisites: Commitment to programming in C/C++ or Fortran Suitability: BSc or MPhys Synchronization is a universal cooperative phenomenon, which occurs, in coupled

self-oscillators. Examples of self-oscillators are clocks, musical instruments, the heart and the brain, single neurons, electronic generators of the signals, and many other artificial and natural objects. Most generally, synchronization means an adjustment of time scales of oscillations in systems due to the interaction between them: if the time scales in the uncoupled systems are not rationally related, introduction of coupling can shift the time scales to make their ratio closer to a rational number n : m, where n and m are integers. This phenomenon is usually referred to as n : m synchronization.

Synchronization plays an important role in a wide range of disciplines, including physics, chemistry, and biology, and is often used as a control tool in engineering applications.

While the theory of synchronization of deterministic systems is quite well developed, theoretical understanding of synchronization in coupled oscillators whose dynamics is induced merely by noise, is still a challenging problem. The student will study various manifestations of synchronization in stochastic systems. The research will involve numerical analysis of stochastic differential equations. From the project the student will learn how to analyse stochastic oscillations in dynamical systems, and will also become familiar with the elements of the theory of stochastic processes and with some basic methods of nonlinear dynamics.

5. Title: Chaotic electron transport in semiconductor superlattice Supervisor: Dr A Balanov Type: Theoretical Prerequisites: Solid State Physics, Mechanics, Commitment to programming is

essential Suitability: BSc or MPhys (suitable for one or two students) Semiconductor superlattices (SLs) are nanostructures made from alternating layers

of two different semiconductor materials, usually with very similar lattice constants, for example, GaAs and AlGaAs. Due to the different energy band gaps of the two materials, the conduction band edge of an ideal superlattice is periodically modulated. The current- voltage characteristics of SLs are usually highly nonlinear due to a variety of quantum-mechanical effects, including resonant tunneling, the formation of Wannier-Stark energy level ladders, and the occurrence of Bloch oscillations. The latter makes SL promising for various applications in ultra high-frequency electronics as generators, amplifiers and detectors of electro-magnetic waves. Recent theoretical and experimental work has revealed that the single-particle trajectories of electrons moving through SL in the presence of a tilted magnetic or alternating electric field can demonstrate very complicated chaotic behaviour, which can counter-intuitively make a significant improvement of transport characteristics of SL [1-3]. A student will be involved in the theoretical research of chaotic electron dynamics in semiconductors and their nanostructures, and physical phenomena associated with single-electron chaos. A significant part of the project consists in computer

simulations based on numerical solutions of a set of ordinary differential equations, hence programming skills are essential. Besides the methods of modeling of electron transport in semiconductor devices, the student will become familiar with different types of oscillations that can occur in nature: periodic, quasiperiodic, and chaotic. This will be a great opportunity to master the basic tools of nonlinear dynamics, including phase trajectory analysis, Poincaré sections, and elements of bifurcation analysis. [1] http://pre.aps.org/abstract/PRE/v77/i2/e026209 [2] http://prl.aps.org/abstract/PRL/v103/i11/e117401 [3] http://prb.aps.org/abstract/PRB/v80/i20/e205318

6. Title: Amplifications of THz radiation in semiconductor nanostructures Supervisor: Dr A Balanov Type: Theoretical Prerequisites: Solid State Physics, Mechanics, Commitment to programming is

essential Suitability: BSc or MPhys (suitable for one or two students) The recent interest in terahertz (THz) science and technology is strongly stimulated

by their various promising applications (see the department webpage: http://www.lboro.ac.uk/departments/ph/research/THz.html ) There exists a strong demand for miniature, coherent, monochromatic, solid-state, room temperature operating sources and amplifiers of THz radiation. A student will be involved in theoretical research devoted to the development of new principles of amplification and generation of THz radiation in quantum nanodevices [1-3] She/he will become familiar with basic tools of the theory of semiconductor superlattices and modelling based on numerical solutions of ordinary differential equations.

[1] http://prl.aps.org/abstract/PRL/v102/i14/e140405 [2] http://prl.aps.org/abstract/PRL/v103/i11/e117401 [3] http://prb.aps.org/abstract/PRB/v80/i20/e205318

7. Title: Using of sound for generation of Terehertz (THz) radiation in

semiconductor nanostructures. Supervisor: Dr A Balanov Type: Theoretical Prerequisites: Solid State Physics, Mechanics, Commitment to programming is

essential Suitability: BSc or MPhys (suitable for one or two students) The presence of deformation waves propagating through solids and associating with

heat transfer and/or sound can be described in terms of quantum quasi-particles known as “phonons”. These quasi-particles can strongly interact with conducting electrons. For example, the frequency response of semiconductor oscillators and detectors is limited by scattering processes including electron-phonon interactions. Surprisingly, though, phonons can serve as a powerful tool for enhancing the electronic and optical properties of solid state devices. E.g., in “SASER” [1], recently developed acoustic analogous to the laser, the amplification of coherent sound waves now opens the new and effective way to control electron transport in nanostructures like

semiconductor superlattice. The student will be involved in the cutting-edge theoretical research on using phonon waves for generation and control of very high-frequency (THz) electron transport in semiconductor nanostructures. The student will become familiar with basic analytical and numerical tools of the theory of semiconductors, of modeling of solid state electronic devices, and of the theory of oscillations and waves. [1] http://prl.aps.org/abstract/PRL/v96/i21/e215504

8. Title: On the physics of topological insulators Supervisor: Dr J Betouras Type: Theoretical Prerequisites: Quantum Mechanics, Solid State Physics Suitability: BSc or MPhys (can be a joint project) In this project the general background of the topological insulators will be discussed

and specific theoretical questions will be worked out. 9. Title: Ferromagnetic Superconductors Supervisor: Dr J Betouras Type: Theoretical Prerequisites: Quantum Mechanics, Solid State Physics, ideally Statistical and

Low Temperature Physics Suitability: BSc or MPhys (can be a joint project) The physics of graphene in magnetic field will be explored with some specific

questions will be worked out theoretically. 10. Title: Graphene in a magnetic field Supervisor: Dr J Betouras Type: Theoretical Prerequisites: Quantum Mechanics, Solid State Physics Suitability: MPhys (can be a joint project) 11. Title: Surface magnetism Supervisor: Dr J Betouras Type: Theoretical Prerequisites: Quantum Mechanics, Solid State Physics, ideally Statistical and

Low Temperature Physics Suitability: BSc or MPhys (can be a joint project) In the framework of Ginzburg-Landau theory of phase transitions, we will discuss how

the magnetization is modified close to surfaces. 12. Title: Reaching stable low temperatures Supervisor: Dr B Chesca Type: Practical Prerequisites: Suitability: BSc (project requires 2 students) Low temperature physics is a well-established and essential element of modern

condensed matter physics. This is because at low temperature most materials have very different properties as compared to room temperature and many surprising and unique phenomena appear, like superconductivity, quantum Hall effect, magnetoresistance anomalies, etc.

Stabilizing the temperature at a value below room temperature is an essential procedure for research at low temperatures. In this project you will be involved in reaching stable temperatures over many hours, even days, in the range, 70 K – 220 K. A recently installed state of the art cryostat is available for this purpose. You will stabilize the temperature inside a VTI (a Variable Temperature Insert) inserted inside the cryostat, via a specially designed temperature controller. You will conclude on the best method out of four available to reach a certain temperature and stabilize it. You will learn about cryogenics procedures using liquid nitrogen.

13. Title: Signal processor/Lock-in amplifier Supervisor: Dr B Chesca Type: Practical Prerequisites: Suitability: BSc The lock-in amplifier has been an important tool for the experimental physicists since

the early 1950’s. It would be unusual to find a research laboratory today that didn’t have at least one lock-in amplifier in use and many more hidden within various measuring instruments. Then signal processing is an important idea for physicists, electrical engineers, physical chemists and biophysicists. For both these reasons it is therefore essential that students who plan to be experimental scientists have hands-on experience with signal processing and understand, particularly, the working of a lock-in amplifier. In this final year project you will use modular device (developed by TeachSpin and named SPLIA1_A instrument) that can be used in a variety of ways to study signal processing. This device must be configured by you and hand adjusted for the particular signal to be studied. In several of is configurations, it can be used as a research grade lock-in with acceptable levels of stability, noise, and dynamic range. However, it was designed as a teaching tool for advances undergraduate of graduate students. It has therefore, many more input and output connectors and the gain, phase shift, frequency, amplitudes, etc, can be controlled by the student. Each function of the device is modular, self-contained. Here are some potential module experiments: preamplifier, filters, detectors, phase shifter, noise generator, reference oscillator. Also possible system experiments include: Test signal, lock-in detection, bridge circuits, light measurements, lock-in detection of magnetic resonance, dc lab amplifier, square wave in sine wave converter, amplitude detector, precision rectifier.

14. Title: Superconducting Quantum Interference Filters: acquisition and

interpretation of experimental data Supervisor: Dr B Chesca Type: Practical Prerequisites: Suitability: MPhys or BSc In the last decade Superconducting Quantum Interference Filters (SQIFs) have been

proposed as high resolution magnetometers. SQIFs are arrays of Josephson junctions with a specially selected distribution of the loop areas. Recently in our department parallel SQIFs have been fabricated from superconducting YBCO thin films deposited on SrTiO bicrystal substrates by PhD student Daniel John under the supervision of Dr Chesca. Daniel measured their current-voltage characteristics at

various low temperatures in the range 4.2 K – 100 K and small magnetic fields. A massive amount of experimental data has been recorded. Anomalies have been observed that needs careful analysis and a solid physical interpretation. The present final year student project consists of a detail investigation of such anomalies using two advanced software programmes like Origin and Excel. A solid physical interpretation of these anomalies would be highly desirable at the end of the project. Publication of the results found are expected to be completed in a top journal of condensed matter physics. Acquisition of new current-voltage characteristics at various low temperatures in the range 4.2 K – 100 K and small magnetic fields may be required.

15. Title: Reactive magnetron sputtering of oxides or nitrides Supervisor: Dr M Cropper Type: Prerequisites: Suitability: MPhys Please see Dr Cropper for further information. 16. Title: Investigation of surface plasmon resonance Supervisor: Dr M Cropper Type: Prerequisites: Suitability: BSc Please see Dr Cropper for further information. 17. Title: Measuring the resistivity of semiconductors with temperature

using a Peltier and four point probe. Supervisor: Dr M Cropper Type: Prerequisites: Suitability: BSc Please see Dr Cropper for further information. 18. Title: Using LEDs and webcams to measure thin films Supervisor: Dr M Cropper Type: Prerequisites: Suitability: BSc Please see Dr Cropper for further information. 19. Title: Can SQIUDs be used as qudits? Supervisor: Dr M Everitt Type: Theoretical/Computational Prerequisites: Strong maths, some ability to program. Suitability: BSc or MPhys Superconducting Quantum Interference Device (SQUID) rings are versatile quantum

devices finding great utility in a broad range of applications ranging from metrology to information processing. They have many fascinating properties, an indication of which can be seen in their energy level diagram as shown below. The question that

this project seeks to address is whether or not they can be readily used as qudits (a many level version of the quantum bit). Note: good programing skills and familiarity with quantum mechanics are essential for this project.

20. Title: Evaluating iPads for Modeling of Quantum Systems Supervisor: Dr M Everitt Type: Theoretical/Computational Prerequisites: Strong maths, good ability to program using an object oriented

language (for example C++, Java). Suitability: MPhys Tablet platforms such as the iPad have become very popular tools for education,

gaming and a whole host of other utilities. Their computational power is often underestimated. For example with the iPad 2, “dual-core Linpack run will yield performance of between 1.5 and 1.65 gigaflops – that’s up to 1.65 billion floating-point operations per second. That raw performance means that the iPad 2 would have remained on the list of the world’s speediest supercomputers until about 1994” [http://www.tuaw.com/2011/05/09/ipad-2-would-have-bested-1990s-era-supercomputers/] (Note: this project will make use of the more powerful “New iPad”). Moreover – the human computer interaction model that most iOS devices employ result in easy to use software. It is the intention of this project to develop an application that would allow a user to solve the time independent Schrödinger equation for an example system, display the results, set/reset parameters and output meaningful graphs of publishable quality. If a sufficiently good program is developed we will look to publish it on the Apple App Store and publish any meaningful findings in, for example, the Journal of Computational Physics. Note: good programing skills (in object orientated languages) and familiarity with quantum mechanics are essential for this project.

21. Title: The quantum to classical transition of a Hamiltonian chaotic

billiard Supervisor: Dr M Everitt Type: Theoretical/Computational Prerequisites: Strong maths, good ability to program Suitability: MPhys or BSc Depending on boundary conditions even single billiards can display dynamical chaos

(extreme sensitivity to initial conditions). An example of one such dynamics is given below. The quantum to classical transition for such systems is a topic of current

neling through the weak link !critical current Ic!2e"), and#0!h/2e . We note that with a characteristic frequency $s!(1/!Cs%s) for the SQUID ring, there is a renormalizedfrequency &s!$s"4'2(2"#0

#2Cs#1$s

#1 related to the #s2

term in a Taylor expansion of the cosine in Eq. !2). Through-out the paper we use Cs!1$10#16 F, %s!3$10#10 H,and '"!0.07#0

2/%s as typical circuit parameters for aSQUID ring in the quantum regime.The em field can be modelled in terms of a cavity mode

using an equivalent circuit comprising a capacitance Ce inparallel with an inductance %e , with a !parallel) resistanceon resonance to define its quality factor. If we assume thisresistance to be infinite we obtain a Hamiltonian for the fieldin terms of the equivalent circuit flux and charge operators,

He!Qe2

2Ce"

#e2

2%e, !3)

where #e and Qe are, respectively, the magnetic flux andelectric charge associated with the cavity. The field fre-quency is $e!1/!Ce%e. For the purposes of simplicity weuse Ce!Cs throughout this paper and specify the frequency$e in each example. We denote as !n* the eigenstates of He .In our numerical work we use a truncated basis with n!0, . . . ,N , where N is taken to be much greater than theaverage number of photons in the system.The em cavity mode and the SQUID ring are coupled

together inductively with a coupling energy given by

H Int!+

%s!#s##x)#e , !4)

where + is a coupling parameter linking the em field to theSQUID ring.We note that by introducing a unitary translation operator

T!exp(#i#xQs /') we can write the Hamiltonian for thering as

Hs!!T†HsT!Qs2

2Cs"

#s2

2%s#'" cos" 2(

#s"#x

#0# . !5)

We also note that, invoking this unitary transformation, theinteraction energy becomes H Int! !(+/%s)#s#e while theem field Hamiltonian remains unaffected. We denote as !,*the !flux-dependent) eigenstates of Hs! . Again in our numeri-cal work we use a truncated basis with ,!0, . . . ,- , where- is taken to be much greater than the average energy levelin which the SQUID operates. The first few eigenvalues (,!0, . . . ,4) of Hs! as functions of #x /#0(!.x) are shownin Fig. 2. As can be seen, although all the eigenvalues are #0periodic in #x , each displays a distinctive functional form in#x . It will become apparent in the following discussion thatthese functional forms take on great importance in determin-ing the behavior of the coupled system at particular points inexternal bias flux.In describing the coupled system, we now introduce the

dimensionless operators xe!!Ce$e /'#e , pe!!1/Ce'$eQe , xs!!Cs$s /'#s , and ps!!1/Cs'$sQs ,together with the lowering and raising operators as

!(1/!2)(xs"ips), as†!(1/!2)(xs#ips) for the ring and

ae!(1/!2)(xe"ipe), ae†!(1/!2)(xe#ipe) for the field. In

terms of these operators the Hamiltonian Ht!!T†HtT for thecoupled system /see Eq. !1)0 can be rewritten in the form

Ht!!'$e" ae†ae" 12 #"'$s" as†as" 1

2 ##'" cos" 2(

#0! '

Cs$sxs"2(.x#

#+

%s! '2

4CsCe$s$e!as†"as)!ae

†"ae). !6)

As an illustrative example we show in Fig. 3 the com-puted, .x-dependent eigenvalues of Ht! for !a) $e!$s !with

FIG. 2. Energy eigenvalues versus .x!#x /#0 for an isolatedSQUID ring.

FIG. 3. !a) Energy eigenvalues versus .x of the SQUID ringHamiltonian Hs !thick lines) and the ring-field total Hamiltonian Ht!thin lines) with $e!$s . The coupling constant +!1/100. Theinset shows an example !arrow) of the lifting of the degeneracy ofthe ring-field levels when +!” 0. !b) as in !a) but with $e!

110$s .

M. J. EVERITT et al. PHYSICAL REVIEW B 63 144530

144530-2

research interest. However, quantum models of such systems usually involve random matrix theory and do not provide examples of the emergence of single classical chaotic trajectories from quantum systems. We will start by developing a detailed understanding of the classical dynamics of this system. This project will move on to using a technique called quantum state diffusion to realise a single such trajectory and seek to determine the criteria for achieving the quantum to classical transition.

Image from http://en.wikipedia.org/wiki/Dynamical_billiards

Note: good programing skills and familiarity with quantum mechanics are essential for this project.

22. Title: Quantifying the Controlling Numerical Error in Newtonian

Gravitating Systems. Supervisor: Dr M Everitt Type: Theoretical/Computational Prerequisites: Ability to program, interest in numeric and parallel programming Suitability: MPhys or BSc Gravitational systems obeying Newton’s Law of Gravity at first appear very simple.

However, due to the vast difference in magnitudes between near and distant particles, even for a few bodies such systems are highly sensitive to numerical error – the system rapidly becoming irreversible. This project will seek to quantify and control such errors.

23. Title: The experimental study of the critical parameters of

Bi2Sr2CaCu2O8+d high temperature layered superconductor. Supervisor: Dr M Gaifullin Type: Practical Prerequisites: General data analysis and programming skills are expected,

general knowledge of electronics, handwork skills and the ability to work independently

Suitability: MPhys or BSc Recently high temperature superconductors find their application in microwave,

optoelectronics, electrical machines such as high field magnets, fault-current limiters, transmission cables, motors, generators. In order to access the full potential of these superconductors a fundamental understanding of the physical processes is needed. Student will gain experience and skills in carrying cryogenic experiment using variable temperature cryostat, using instruments under computer control, learn how to compare and fit experimental data with the theoretical results, will study the process of preparation of ohmic contacts for current-voltage and resistance

measurements of superconducting samples. The bachelor thesis project should investigate in detail the critical parameters of Bi2Sr2CaCu2O8+d superconductor such as critical temperature and critical current.

24. Title: The experimental study of the in-plane transport properties of

Bi2Sr2CaCu2O8+d high temperature layered superconductors. Supervisor: Dr M Gaifullin Type: Practical Prerequisites: General data analysis and programming skills are expected,

general knowledge of electronics, handwork skills and the ability to work independently

Suitability: BSc Recently high temperature superconductors find their application in microwave,

optoelectronics, electrical machines such as high field magnets, fault-current limiters, transmission cables, motors, generators. In order to access the full potential of these superconductors a fundamental understanding of the physical processes is needed. Student will gain experience and skills in carrying cryogenic experiment using variable temperature cryostat, using instruments under computer control, learn how to compare and fit experimental data with the theoretical results, will study the process of preparation of ohmic contacts for current-voltage and resistance measurements of superconducting samples. The bachelor thesis project should investigate the anisotropy of the transport properties of Bi2Sr2CaCu2Ox superconductor single crystals.

25. Title: The experimental study of the intrinsic Josephson effect in

Bi2Sr2CaCu2O8+d superconductor single crystals. Supervisor: Dr M Gaifullin Type: Practical Prerequisites: General data analysis and programming skills are expected,

general knowledge of electronics, handwork skills and the ability to work independently

Suitability: MPhys or BSc Josephson effect is widely used in the generation and detection of microwave

radiation, it is used in voltage standards in metrology, in superconducting microprocessors, in quantum computers. To exploit the full potential of this effect, the understanding of physical processes is necessary. Students will gain experience and skills in conducting an experiment using a cryogenic variable temperature cryostat, microwave generators, using devices under computer control, learn how to compare and fit experimental data with the theoretical results, will study the process of manufacturing the Josephson junction. The bachelor thesis project should investigate in the detail the properties of intrinsic Josephson junctions in Bi2Sr2CaCu2O8+d superconductor single crystals. The main experimental method is based on DC measuring the tunneling currents vs. voltages and microwave measurements.

26. Title: The experimental study of the transport properties of Bi2Sr2CaCu2O8+d high temperature layered superconductors in magnetic field.

Supervisor: Dr M Gaifullin Type: Practical Prerequisites: General data analysis and programming skills are expected,

general knowledge of electronics, handwork skills and the ability to work independently.

Suitability: BSc Recently high temperature superconductors find their application in microwave,

optoelectronics, electrical machines such as high field magnets, fault-current limiters, transmission cables, motors, generators. In order to access the full potential of these superconductors a fundamental understanding of the physical processes is needed. Student will gain experience and skills in carrying cryogenic experiment using variable temperature cryostat, using instruments under computer control, learn how to compare and fit experimental data with the theoretical results, will study the process of preparation of ohmic contacts for current-voltage and resistance measurements of superconducting samples. The bachelor thesis project should investigate the effect of magnetic field on the transport properties of Bi2Sr2CaCu2O8+d superconductor single crystals. The main experimental method is based on resistivity measurements.

27. Title: Investigation of the Runaway Greenhouse Effect Supervisor: Dr R Giles Type: Theoretical Prerequisites: Suitability: BSc The end of life on Earth will arrive when the brightening Sun crosses the threshold at

which the water-vapour greenhouse effect runs away causing the oceans to boil dry. At least one eminent scientist believes that if man burns all the fossil fuel reserves then the run-away threshold will be exceeded. This project will investigate the run-away greenhouse effect starting with a simple radiation model which can be solved analytically; this will lead on to computer coding so as to make use of a full-scale radiation model.

28. Title: Extracting Energy from Sunlight Supervisor: Dr R Giles Type: Theoretical Prerequisites: Suitability: BSc Artificial photosynthesis is an active field of research as it could potentially be a large

source of renewable energy. This project will conduct the initial investigation of one mechanism by which some kind of artificial photosynthesis might be achieved. The idea is to use a chain, or array, of nanomagnets to extract energy from sunlight and transfer the energy to charge oscillations in a metal. The project will involve developing a computer program to model the behaviour of a group of nanomagnets in an oscillating magnetic field and analysing the results produced. The student should be taking the Condensed Matter Physics module and be

comfortable with writing computer programs. The project is the idea of Dr Mike Forrester and he will be supervising it jointly with me.

29. Title: Gravitational Waves Supervisor: Dr D Guleivch Type: Theoretical Prerequisites: Suitability: Gravitational waves are ripples of curvature of spacetime propagating in empty

space. Although, not any signature of gravitational wave have been detected yet, they are predicted by as solutions of the Einstein field equation in General Relativity. The project will also focus on the theory of how gravitational waves are generated, why gravitational waves can be measured at all and how the detectors work. The aim of the project is to critically investigate the existing methods of detection of gravitational waves, also, to produce an up-to-date survey of the many exciting possibilities of the sources that are likely to produce detectable waves, such as colliding black holes or rapidly spinning neutron stars.

30. Title: Thermodynamics of black holes Supervisor: Dr D Gulevich Type: Theoretical Prerequisites: Suitability: Black holes arise as solutions to the Einstein fields equation in General Relativity and

posses many extraordinary physical properties. The student is invited to investigate the thermodynamics of a black hole and calculate its entropy.

31. Title: Calculation of zero-point energy of the vacuum Supervisor: Dr D Gulevich Type: Theoretical Prerequisites: Suitability: The zero-point energy of the vacuum is believed to be responsible for the

Cosmological constant. The aim of the project is to get insight into zero-point fluctuations and their relation to the Casimir effect, the Lamb shift and the Cosmological constant. References: G. Mahajan, S. Sarkar, and T. Padmanabhan, “Casimir Effect confronts Cosmological Constant”, arXiv:astro-ph/0604265v1.

32. Title: Theoretical study of magnetic monopoles in spin ices Supervisor: Dr D Gulevich Type: Theoretical Prerequisites: Suitability: Magnetic monopoles are charges of magnetic field predicted to have formed in the

very early Universe. Although, real magnetic monopoles have not been detected, scientists now able to create quasiparticles which behave in a similar way as real charges of magnetic field. Such quasiparticles may only exist in materials called spin ices. The aim of the project is to investigate the properties of gas of such quasipartlices in spin ices.

33. Title: Measurement and Analysis of the Rotation Curve for the Milkyway

Supervisor: Dr D Gulevich / Phil Sutton Type: Practical Prerequisites: Compulsory Physics with Cosmology programme, astronomy

and cosmology modules. Suitability: BSc The 21cm line produced by neutral hydrogen in interstellar space provides radio

astronomers with a very useful probe for studying the differential rotation of spiral galaxies. Radial velocities for the neutral hydrogen line are calculated by measuring the Doppler shift in the 21cm line. By observing hydrogen lines at different points along the Galactic plane one can show that the angular velocity increases as you look at points closer to the Galactic centre. The purpose of this experiment is to create a rotational curve for the Milky Way Galaxy using 21cm spectral lines observed with a small radio telescope, including interoperation of results and its role in the dark matter problem. The observations for this experiment will be made using the 3m radio telescope located on the roof of the physics building. The rotational curve will be created by plotting the maximum velocity observed along each line of sight versus the distance of this point from the Galactic centre. The practical work for this project is to be carried out in semester one.

34. Title: Measurement of the Differential Solar Rotation Period Supervisor: Dr D Gulevich / Phil Sutton Type: Practical Prerequisites: Compulsory Physics with Cosmology programmes, astronomy

and cosmology modules. Suitability: BSc Solar rotation is able to vary with latitude because the Sun is composed of a gaseous

plasma. The rotation is observed to be fastest at the equator and to decrease as latitude increases towards the poles. The rotation of the Sun at different latidutes will be investigated by imaging of the Sun and any sun spots using various dedicated solar telescopes. The change in longitude per day of sunspots will be used in the determination of the rotation periods. By observing the movement of sunspots on the surface of the Sun we hope to calculate the angular rotation velocity at differing latitudes, concentrating on the difference between the two hemispheres.

35. Title: Graphene Project 1 Supervisor: Prof F Kusmartsev Type: Theoretical Prerequisites: Suitability: Graphene is the world’s thinnest material at just one atom thick. Discovered in 2004

this material open a new page in the Material Science. Graphene represents a conceptually new class of materials, which exhibits exceptionally high crystal and electronic quality and, has already revealed many potential applications. It has unusual electronic spectrum, which gave a new paradigm of “relativistic” physics, which can be tested in laboratory experiments. This new material exhibits exceptionally high crystal and electronic quality and, despite its short history, has already revealed many potential applications.

It was, Peierls and Landau, who first in 1935 and in 1937, respectively and

independently proved that two-dimensional crystals are thermodynamically unstable and could not exist[1,2]. Their theory pointed out that a divergent contribution of short-ranged thermal fluctuations in low-dimensional crystal lattices should lead to such displacements of atoms that they become comparable to interatomic distances at any finite temperature [3]. The argument was later extended by Mermin [4] (so-called, the Mermin Theorem) and is strongly supported by a huge amount of experimental observations. Indeed, the melting temperature of thin films rapidly decreases with decreasing thickness, and they become unstable (segregate into islands or decompose) at a thickness of, typically, a few atomic layers [5,6]. For this reason, atomic monolayers have so far been known only as an integral part of larger three-dimensional structures, usually grown epitaxially on top of monocrystals with matching crystal lattices [5,6]. Without such a 3D base, 2D materials must not exist. Since 2004, it was argued that the common wisdom was flaunted by the experimental discovery of graphene and other freestanding 2D atomic crystals (for example, single-layer boron nitride and half-layer BSCCO)[7,8]. These crystals could be obtained on top of non-crystalline substrates [8-10], in liquid suspension [7,9] and as suspended membranes [11]. The project investigates how this contradiction between the theory comprising well known theorems and discovery of graphene can be compatable.

The finding of possible lattice distortions which can stabilize the two-dimensional crystal structures of the graphene and at the same time do not change the graphene relativistic spectrum [12] will be a of great importance for the next developing of this material and will form a firm basis to the next future numerous application.

The developing of this material knowledge will benefit business, consumers and science communities.

36. Title: Graphene project 2 Supervisor: Prof F Kusmartsev Type: Theoretical Prerequisites: Suitability: Various graphene electronic devices will be studied as well as graphene optics.

In particular the student will consider a few simple models how electron interacts with phonons. Here various electron-phonon and electron-photon interaction in graphene will be considered. In particular, De Haas van Alphen or Shubnikov de Haas oscillations should be studied. The project is considered as extremely important for student developments as well as carries large scientific and intellectual load.

37. Title: Graphene project 3 Supervisor: Prof F Kusmartsev Type: Theoretical Prerequisites: Suitability: Electronic diffraction phenomena in graphene. Here will be considred different

Nanostructures and propagation of electron through these structures. A particular attention will be dedicated to Aharonov-Bohm effect. Bozonisation methods will be also studied. This project is more mathematical and should only be chosen by students who love to do mathematical calculations.

38. Title: Graphene project 4 Supervisor: Prof F Kusmartsev Type: Theoretical Prerequisites: Suitability: Mermin-Wagner theorem and stability of the flat structures of the grapheme since it is

expected that novel graphene technology in near future will replace the modern Si technology.

This project will be intended to perform in a framework of the Research school of materials.

It is expected also that Maths Department will be involved.

1. Peierls, R. E. Quelques proprietes typiques des corpses solides. Ann. I. H. Poincare 5, 177-222 (1935).

2. Landau, L. D. Zur Theorie der phasenumwandlungen II. Phys. Z. Sowjetunion, 11, 26-35 (1937).

3. Landau, L. D. and Lifshitz, E. M. Statistical Physics, Part I. Pergamon Press, Oxford, 1980.

4. Mermin, N. D. Crystalline order in two dimensions. Phys. Rev. 176, 250-254 (1968).

5. Venables, J.A., Spiller G.D.T., Hanbucken, M. Nucleation and growth of thin films. Rep. Prog. Phys. 47, 399-459 (1984).

6. Evans, J.W., Thiel, P.A., Bartelt, M.C. Morphological evolution during epitaxial thin film growth: Formation of 2D islands and 3D mounds. Sur. Sci. Rep. 61, 1-128 (2006).

7. Novoselov, K. S. et al. Electric field effect in atomically thin carbon films. Science 306, 666-669 (2004).

8. Novoselov, K. S. et al. Two-dimensional atomic crystals. Proc. Natl Acad. Sci. USA 102, 10451-10453 (2005).

9. Stankovich, S. et al. Graphene-based composite materials. Nature 442, 282-286 (2006).

10. Meyer, J.C. et al. The structure of suspended graphene sheets. Nature (in press, 2007).

11. Nelson, D. R., Piran, T. and Weinberg, S. Statistical Mechanics of Membranes and Surfaces. World Scientific, Singapore, 2004.

12. Partoens, B. and Peeters, F.M. From graphene to graphite: Electronic structure around the K point. Phys. Rev. B 74, 075404 (2006)

39. Title: Methods of Statistical Mechanics to Investigate Distribution of Wealth Supervisor

Supervisor: Prof F Kusmartsev Type: Theoretical Prerequisites: Suitability: Using the methods of statistical mechanics to investigate different distribution of

income, money and wealth in different countries and find indications of financial crisis in these data. Simulation of some simple theoretical models is expected. Knowledge of statistical physics is desirable but can be learned in the course of the project job.

40. Title: Polarons Supervisor: Dr J Samson Type: Theoretical/Computational Prerequisites: Good knowledge of quantum mechanics, good programming

ability Suitability: MPhys As an electron moves through a crystal, it attracts the positive ions towards itself.

The combination of electron and lattice distortion, known as a polaron, moves through the solid. It has a lower bandwidth (higher effective mass) than the electron on its own. Such electron-lattice interactions are an essential part of the theory of conventional superconductors, and may play an important role in high temperature superconductors. The main approach to be followed involves Monte Carlo simulations: spin a roulette wheel (or generate random numbers) and take an average of some quantity over a large number of trials. In this context an electron is allowed to hop at random, with the effect of a lattice distortion taken into account, and properties of the polaron deduced by observing how far the electron moves. The code for this already exists. A simpler model, involving a diatomic molecule rather than a solid, was investigated in 2002 by a final-year student using a different Monte Carlo technique (diffusion Monte Carlo) that involves solving Schrödinger’s equation: allow a large number of particles to make random walks. Let them multiply where the potential is low and disappear where the potential is high. They will come to an equilibrium distribution where the piling up at the minimum of a potential is balanced by the diffusion out of this minimum. The distribution turns out to be the ground state wave function. Project specification The project will involve simulation, analysis and development of the simpler model of an electron in a diatomic molecule, with possible extension to larger systems. These results will be compared with those for an electron in a lattice obtained as a result of a recent EPSRC research project (see papers by Hague et al below). Background reading Steve Gumbrill, Quantum Monte Carlo solution of Schrödinger’s equation, BSc final year project 2002 Alexandrov A S and Mott N F, Polarons and Bipolarons (World Scientific, 1996) Spencer P E, Samson J H, Kornilovitch P E and Alexandrov A S, Effect of electron-phonon interaction range on lattice polaron dynamics: a continuous-time quantum

Monte Carlo study, Phys Rev B71 184310 (2005) Hague J P, Kornilovitch P E, Alexandrov A S and Samson J H, Effects of lattice geometry and interaction range on polaron dynamics., Phys Rev B73 054303 (2006) Hague J P, Kornilovitch P E, Samson J H and Alexandrov A S, Superlight small bipolarons in the presence of a strong Coulomb repulsion, Phys Rev Lett 98 037002 (2007) Hague J P, Kornilovitch P E, Samson J H and Alexandrov A S, Superlight small bipolarons, J Phys: Condens Matter 19 255214 (2007)

41. Title: Quantum computing on a classical computer Supervisor: Dr J Samson Type: Theoretical/computational Prerequisites: Quantum Computing Suitability: MPhys A quantum computer relies on the massive parallelism inherent in superpositions of

states. An n-bit register in a classical computer can hold one of 2n numbers, and only one such number at a time. A quantum register with n qubits (n two-state systems) can hold all 2n values simultaneously, and a quantum algorithm can operate on all these in parallel and can in principle operate exponentially faster than a classical computer for certain problems. The user can only extract n bits of information, which severely limits the range of problems. The most famous quantum algorithm is Shor’s prime factorisation algorithm: on a classical computer, the time taken to factorise an n-bit number increases exponentially with n, while Shor’s algorithm will do this quickly on a quantum computer. This would render current Internet encryption technology insecure. Previous project students simulated part of the Shor algorithm. Another, somewhat simpler, quantum algorithm is Grover’s database search, which finds a marked item in a database of N items by looking only about √N times. Project specification Building a quantum computer is beyond the scope of this project. However, it is possible to simulate a quantum computer with a classical computer (although this will not be as fast as solving the problem on a classical computer in the first place). There are several possible directions of the project: 1 Simulate the Shor factorisation algorithm and establish the probability of a successful factorisation. 2 Simulate Grover’s database search algorithm. Here it is possible to include the effects of decoherence in the simulations (i. e., noise and other inevitable unwanted interactions with the environment which introduce errors). Previous students have written code to simulate these algorithms and introduce noise, but the results are not yet understood. 3 Try some other algorithm from the literature. Background reading Nielsen M A and Chuang I L Quantum Computation and Quantum Information (CUP, 2000) See material for PHC130 Fundamentals of Quantum Information and PHD230 Quantum Computing on http://learn.lboro.ac.uk/. Matt McQuade and Laurence Perkins, Quantum Computing with a Classical Computer, BSc final year projects 2005 (on Shor)

Alex Collins and Mital Patel, Quantum Search: Modelling Grover’s Search Algorithm, BSc final year projects 2006 (on Grover) Jamie Edwards, Quantum Computing with a Classical Computer, BSc final year project 2009 (on Shor)

42. Title: Adiabatic quantum computing Supervisor: Dr J Samson Type: Theoretical/computational Prerequisites: This project would suit a student with strong mathematical skills

and programming experience (preferable in C/C++). The student should have taken (or be taking) Quantum Computing.

Suitability: MPhys A novel approach to using quantum mechanics to solve computational problems is to

encode the problem in the Hamiltonian of a physical system (for example, a collection of spins) in such a way that the ground state wave function encodes the solution. If a sufficiently strong magnetic field is applied, the spins will align at zero temperature. If the field is turned off slowly, the system remains in the ground state (see Fig 1) and the solution can be read off. However, there is a non-zero probability that the wrong answer is obtained; the slower the time evolution, the smaller this error probability. This is a new area with many open questions, such as the type of problem for which the method will be useful and the factors that determine the probability of success. Two project students (Martyn Ormerod and Mike Cullimore) have recently studied the probability of error of the algorithm given a random problem; the results have been submitted for publication (Cullimore et al 2011). The scatter plots (Fig 2) show a remarkable structure, which we are still trying to understand.

Fig 1: The Hamiltonian evolves slowly from a simple form H1 at b=0, with known ground state, to a complex one H0 at b=1, whose ground state is computationally hard to determine. Energy levels are shown vertically. If the time evolution is sufficiently slow the system evolves adiabatically and therefore remains in the ground state. Figure courtesy Zagoskin and Savel’ev.

Fig 2: Scatter plot of success probability against minimum gap between ground and first excited state for a large sample of 2-qubit Hamiltonians. Colour scheme represents interaction strength between qubits. From Cullimore et al (2011)

Project specification The project will involve simulation and theoretical modelling of adiabatic quantum

computation. In particular, we hope to learn the features of problems that are well suited to adiabatic algorithms. Background reading Seb Pinski, Richard Wilson, MPhys final year projects 2008; Charles Lamdin, MSc project 2009 Martyn Ormerod, MPhys final year project 2010; Mike Cullimore, MPhys final year project 2011 M Cullimore, M J Everitt, M A Ormerod, J H Samson, R D Wilson and A M Zagoskin, The relationship between minimum gap and success probability in adiabatic quantum computing, arXiv:1107.4034 (2011)

43. Title: Self-organised criticality Supervisor: Dr J Samson Type: Computational/experimental Prerequisites: Programming data analysis. Imagination and observation

suggesting other systems to model would help. Suitability: BSc or MPhys

Introduction If a simple system behaves in a complicated way, we call it chaos; if a complicated system behaves in a simple way we call it self-organisation. Many complex systems, such as the earth’s crust, organise themselves to be on the edge of stability and then show simple behaviour. Changes, such as earthquakes, occur at all length scales and may show characteristic power spectra such as the 1/f noise seen in a wide number of other contexts. Previous students a long time ago simulated a model of raindrops running down and coalescing on a window pane, which was believed to show similar behaviour: after a long time, there should be a steady-state distribution. This distribution should show certain scaling properties: further down the window, there should be a similar distribution but with a smaller density of larger drops. The results were inconclusive, and it is worth revisiting the problem with current computer technology. There is scope for further work in related problems and experimental work. Project specification You will model a physical system (the raindrop problem or any another related problem that may emerge from discussions — use your imagination here) and conduct a detailed analysis of the data. It may also be possible to carry out experimental work to test your models. Background reading Jensen H J, Self-organised criticality, (Cambridge University Press, 1998) Chris Creasey, Self-organised criticality, BSc project report 1992 Ben Leil, A Computer Simulation of a self organised critical system, BSc project report 1994

44. Title: Spooky action at a distance Supervisor: Dr J Samson Type: Theorectical/computational Prerequisites: Fundamentals of Quantum Information. Programming skills;

ability to think outside the box also useful. Suitability: BSc or MPhys

Introduction In the Einstein-Podolsky-Rosen (EPR) experiment, an atom emits two electrons in a singlet (i. e., antiparallel-spin) state. These two electrons are entangled: although no longer interacting, their states are correlated in such a way that measurement of, say, the z component of spin of the first to be Sz=½ instantaneously collapses the wave function of the other so that it will have Sz=–½ if measured. Einstein was not happy with this “spooky action at a distance”. One interpretation of this (outside the Copenhagen interpretation of quantum mechanics) is that there are hidden variables (secret instructions) determining the result of any measurement: each pair chooses an instruction manual at random and tears it in two, with each electron taking half the manual. This manual predetermines the outcome of the measurement of spin in any direction. However, Bell showed that this is incompatible with the predictions of quantum mechanics for certain settings of the detectors, and the experiment of Aspect was consistent with the quantum result and inconsistent with the hypothesis that the electrons have a definite direction before measurement. Thus there is no classical way in which a pair of electrons can reproduce the behaviour of entangled electrons. Such entangled pairs are a fundamental part of quantum communication. They allow two parties to share quantum information, and can be used to transmit the quantum state of an object with neither party being aware of what the state is (quantum teleportation). Some may jump to the conclusion that the instantaneous non-local collapse of the wave-function can transmit information faster than light. This is not true. The experiment satisfies the no-signalling principle: because the result of the measurement is random, the act of measurement of one spin cannot be used to transmit classical information to the other spin. Indeed there are other models (such as the Popescu-Rohrlich box) that are even more correlated than quantum entanglement allows, but still do not permit signalling. Project specification This is a numerical simulation of the EPR experiment and variations of it. It should be possible to generate sample results both for hidden variable theories, for standard quantum mechanics and more strongly correlated theories, to test the Bell inequalities in all cases, and to simulate the experimental conditions. You can investigate how far classical principles need to be violated to reproduce the quantum results (for example, by assuming that some spin directions occur with probability less than zero). It will also be possible to model quantum communication and teleportation protocols. Background reading Rae A I M Quantum Physics: Illusion or Reality? (CUP, 2004, 530.12/RAE), final chapter Mermin N D Boojums all the way through (CUP, 1990, 530/MER), part II Bell J S Speakable and Unspeakable in Quantum Mechanics (CUP, 2004, 530.12/BEL) Rafael Ginoux & Ian Saggers, BSc project reports 2003 Ash Cooper, BSc project report 2011

45. Title: How random is chaos? Supervisor: Dr J Samson Type: Theoretical/computational Prerequisites: Programming and data analysis ability are needed. Suitability: BSc or MPhys

Introduction Given experimental data — the flow of a fluid, lottery numbers, etc. — how can we tell if they are random? Simple dynamical systems with few degrees of freedom (such as a periodically driven damped pendulum) can appear random at first sight. However, the behaviour is deterministic and can be described in terms of a small number of variables obeying Newton’s laws. There are algorithms for measuring the dimension of the attractor; essentially, how many degrees of freedom are important. If this number is small, we may have regular or chaotic behaviour; if it is large, such as in a fluid at high Reynolds numbers, we have turbulence; if it is infinite, we have truly random behaviour. Final-year project students have developed code to calculate such dimensions and have shown, for example, that random number generators aren’t while lottery draws are. Given the increase in computational power available, much deeper analysis is now possible. There is scope for further selection and analysis of data and analysis of chaotic systems. Project specification 1 Gathering of data; suitable sources are weather statistics, digits of π, stock market prices, numerical simulations of differential equations, “random”-number generators, nonlinear electrical circuits. The choice is yours. 2 Coding of time-series analysis 3 Analysis and interpretation of results Background reading Peitgen, Jürgens and Saupe Chaos and Fractals (Springer, 1992, 003 PEI) Phil Sermon, BSc final year project 1997 Andy Crabtree, Fractal dimensions in complex systems BSc final year project 1999 Alec Edworthy & Neil Papworth, How random is chaos?, BSc final year project 2002

46. Title: Percolation Supervisor: Dr J Samson Type: Computational or experimental Prerequisites: This project would suit a student with good data analysis and IT

skills (preferably a programming language). Science of the Internet (for graph theory) and Statistical and Low Temperature Physics are useful. The balance between experimental work, data analysis and computer modeling can be varied to suit the students requirements. There is scope for experimental work in conjunction with numerical modeling; two students may therefore work on different aspects.

Suitability: BSc (single or pair)

Introduction Take a large square array of points and start wiring up neighbouring pairs of points at random. Measure the conductivity between opposite faces. At what point will a current start to flow? (The answer in this case: when a fraction 50% of the bonds is connected.) Or take a mixture of iron filings and sand: how does the conductivity

depend on the concentration p of iron filings? (Answer: when the current starts flowing it behaves like a power law, σ ∝ (p-pc)β, where β, the critical exponent, is a number of order 1 that is identical for a broad range of systems and pc is the critical concentration.) Or you want to extract oil out of porous rock: what fraction of the oil can you get out? Or how many nodes do you have to remove for the Internet to break down? These are all examples of percolation theory. Previous students have carried out experiments on resistor networks and modelled them in Excel with the help of macros, or in C, obtaining an excellent fit.

  Fig 1: Resistor network Fig 2: Experimental conductance of 5 × 5 network (Zheng) Project specification The proposal is to investigate the distribution of the residual potential once the resistors have been removed; I don’t know if this is in the literature. (For the sake of argument picture a capacitor at every node so that the system recalls the final voltage when the last resistor was removed.) In order to obtain good statistics in and allow quantitative conclusions it is necessary to code the model in C++ or a similar language. Background reading Ziman J M, Models of Disorder (CUP, 1979, 530.4/ZIM) Mat Jones, BSc final-year project 2005 Lan Zheng & Maame Gyesi-Appiah BSc final year projects 2007 Neil Morgan & Penny Taylor, Percolation, PHC186 project 2010 Jack Nash, BSc final-year project 2011

47. Title: How large is the Earth? Supervisor: Dr J Samson Type: Theoretical/data analysis/computational Prerequisites: Mathematical ability and good facility with differential equations;

may suit a Physics and Maths student or Strong IT/programming skills.

Suitability: BSc (single or pair)

Introduction Apparently the Southern Uplands of Scotland have been seen from Snowdonia in North Wales, even though the straight-line path between them would go below sea level. This is due to atmospheric refraction — see figure 1 — and can be represented as an increase in the effective radius of the Earth.

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Figure 1: effect of atmospheric refraction on line of sight

The effective radius depends somewhat on atmospheric conditions. Jonathan de Ferranti (Viewfinder Panoramas, http://www.viewfinderpanoramas.org/) has produced panoramas from numerous viewpoints with the use of a mapping database. He assumes a 20% increase in the effective radius of the Earth. See figure 2 below showing the view from Mt Whitney, California (distances in mi = 1.609 km) and the gallery on the above web site.

Figure 2a Theoretical view from Mt Whitney © de Ferranti

Figure 2b Observed view from Mt Whitney © Samson

Previous students have already produced a spreadsheet that determines the

distance to the horizon and light path for a realistic atmospheric model, and have obtained analytical results for simple models of the atmosphere. Terrain data are available online; however, it has proved difficult to extract it from the files in a useable format. The project therefore requires good IT skills. Project specification There are two options, so it may be possible to accommodate two students on the project: 1 Development of a continuum theory (differential equation for the light path) 2 Merging published altitude data with the spreadsheet Background reading Dave Batchelder & Adam Pearce (2006), Richard Ogle (2007), Richard Ewin (2008), Dave Cook (2010), Matt Green (2011) BSc project reports

straight line

line of sight

48. Title: Biologically inspired solid state nanodevices Supervisor: Dr S Saveliev Type: Prerequisites: Suitability: The manipulation of tiny particles in nanodevices, which are strongly influenced by

noisy environment, has required novel approaches to control their motion. Recent experiments on transport of K and Rb ions in an ion channel and particles of different size in asymmetric silicon pores inspire novel way [1] to move particle in nanodevices using asymmetric spatial-temporal potentials. A student will be involved in simulations of dynamics of tiny particles using Langevin differential equations. Different regimes of motion will be studied.

49. Title: Modelling price dynamics by using ARCH stochastic process Supervisor: Dr S Saveliev Type: Prerequisites: Suitability: The problem of the distribution of price changes has been considered by both

physicists and mathematicians since the 1950s. Now this problem attracts particular attention since solving it we will be able to both minimize potential financial risks and get a deeper view on the evolution of very complex non-equilibrium systems. Two most promising stochastic models describing price dynamics and time-dependent price volatility are so called ARCH and GARCH models. ARCH processes are empirically motivated discrete-time stochastic models for which the variance at time t depends, conditionally, on some past values of the square value of the random signal itself. ARCH models have been applied to several different areas of economics, including (i) mean and variance of inflation in the UK, (ii) stock returns, (iii) interest rates, and (iv) foreign exchange rates. We will study how changing conditional probability in ARCH processes affects the price dynamics and will try to find the probability distribution which fits real price dynamic.

50. Title: Modelling price dynamics by using GARCH stochastic process Supervisor: Dr S Saveliev Type: Prerequisites: Suitability: The statistical properties of the time evolution of the price play a key role in the

modelling of financial markets. For example, the knowledge of the stochastic nature of the price of a financial asset is crucial for a rational pricing of financial derivatives. Based on theoretical and empirical analysis several alternative models have been proposed. Two most promising stochastic models describing price dynamics and time-dependent price volatility are so called ARCH and GARCH models. ARCH processes are empirically motivated discrete-time stochastic models for which the variance at time t depends, conditionally, on some past values of the square value of the random signal itself. GARCH process is the generalization of ARCH model allowing to describe price data by a much smaller number of parameters. We will study how changes of GARCH processes’ parameters affect price correlations and price volatility.

51. Title: Taxonomy of stock-portfolio Supervisor: Dr S Saveliev Type: Prerequisites: Suitability: Taxonomy of a stock portfolio is hierarchical structure or classification scheme

allowing a trader or portfolio holder to optimize his/her stock portfolio according to a trading strategy he/she uses strategy. We plan to analyse time correlations of different stocks to construct taxonomies of different real stock portfolio (e.g., Dow Jones Industrial Average) as well as different currency portfolio by using Kruskal's algorithm of graph theory.

52. Title: Bose-Einstein Condensation Supervisor: Dr B Sobnack Type: Prerequisites: Suitability: Please see Dr Sobnack for further information. 53. Title: Quantum Evaporation from Superfluid Helium Surfaces Supervisor: Dr B Sobnack Type: Prerequisites: Suitability: Please see Dr Sobnack for further information. 54. Title: How to boil an egg? Supervisor: Dr B Sobnack Type: Prerequisites: Suitability: Please see Dr Sobnack for further information. 55. Title: Electron transport in Graphene Supervisor: Dr B Sobnack Type: Prerequisites: Suitability: Please see Dr Sobnack for further information. 56. Title: Stress Measurement in Polymer Composites Supervisor: Dr G Swallowe Type: Prerequisites: Suitability: MPhys Composites consisting of a polymer matrix and either fibre or particulate fillers are

widely used as structural materials. Although overall stress levels can be measured, actual measurement of the stress distribution in the composite is very difficult. Observations of Bragg reflection peak shape changes in neutron diffraction

experiments suggest that these shape changes may provide a method of measuring these stresses. Similarly Raman peak shifts are observed in polymers under load and this may provide a route to measure stresses. During 20010/11 experimental rigs were developed for use with an X-ray diffractometer and the Raman spectrometer to investigate this possibility. Preliminary results indicate that stress measurements may be feasible but more work is needed on both techniques.

57. Title: Effect of Electric Field on Bubbles Supervisor: Dr G Swallowe Type: Prerequisites: Suitability: It has been observed that bubbles (both soap bubbles and droplets) deform when

subjected to a large electric field. The purpose of this project is to experimentally investigate the behaviour of bubbles and droplets in DC electric fields. The project will involve the design and construction of apparatus to generate suitable bubbles and hold them in an electric field whilst making measurements of bubble dimensions. A range of differing fluids (conducting/non-conducting/various surface tensions) will be used so that a comprehensive data set can be obtained for comparison with theory.

58. Title: Measurements of Liquid Surface Properties from Surface

Acoustic Waves Supervisor: Dr G Swallowe Type: Prerequisites: Suitability: In recent years, many techniques have been used to investigate the characteristics of

the surface acoustic wave (SAW), providing a large amount of information on the material surface. These have been mainly concentrated on studies of solid surfaces. Weisbuch and Garbay considered the liquid SAW as a diffraction grating and devised up an optical method to detect the liquid surface tension. (Am. J. Phys 47, 355 (1979)) Generally speaking, the diffraction pattern distributes symmetrically. But using low-frequency liquid surface wave, not only steady and visible diffraction patterns were obtained, but also obvious asymmetry of diffraction patterns was observed. This project is intended to reproduce the results of earlier workers on SAWs in liquids and, in particular, investigate asymmetries in the observed diffraction patterns. Results obtained will be compared to theoretical explanations of the asymmetries and the possible application of the technique for measuring the damping constant of liquid surface wave. The project involves the design and construction of suitable apparatus and it’s use to gather data suitable for comparison with previous work and theoretical predictions.

59. Title: Fatigue in paintings Supervisor: Dr G Swallowe Type: Prerequisites: Suitability: The effect of vibration on works of art is a matter of concern. Although it is recognised

that vibration can be damaging to artworks, a direct relationship between the extent of vibration and damage to paintings has never been made. Severe vibration can cause direct physical changes to sensitive artworks such as structural cracking,

delamination and paint loss but high stresses are involved. However, repeated, smaller amplitude cycles of stress can lead to progressive structural damage in the paint layers at the micro level known as fatigue. Material fatigue accumulates with time and eventually the localised damage in the paint layers will reach a critical level and the material will fail i.e. fracture. The cumulative effect of vibration means that damage can occur after long periods of time, and not just one short event. Visitor circulation, city traffic, nearby building works etc. generate vibration on a daily basis, which will continuously add to the number of vibration cycles that the artwork has already experienced. Vibrations from these sources travel through the rigid building structure to the walls upon which paintings are displayed and are then transmitted to the painting. Fatigue damage has been noted on several recent occasions when building works have taken place within or adjacent to museums. A characteristic of fatigue is that the lower the amplitude of vibration, the longer it takes for damage to occur but there are virtually no studies of the fatigue properties of paint and/or paint on the painting support (usually canvas, wood panel or paper). The aim of the project is to design and utilise suitable experimental techniques to investigate this problem. This project builds on experience gained during a 2011/12 project where initial trial measurements and techniques were explored.

60. Title: Adiabatic invariants in quantum computing Supervisor: Dr A Zagoskin Type: Prerequisites: Suitability: Adiabatic invariants are the dynamical variables, which do not change when the

system undergoes a slow external perturbation. You will investigate the role of adiabatic invariants in a quantum system consisting of qubits.

61. Title: Weak measurements of the quantum state of a superconducing

qubit Supervisor: Dr A Zagoskin Type: Prerequisites: Suitability: A weak measurement of a quantum state takes place when the quantum system is

only weakly coupled to the detector and the wave function "collapse" is gradual, and not instantaneous. You will model and analyze different realizations of the weak measurement of a superconducting qubit.

62. Title: Quantum heat engine simulation Supervisor: Dr A Zagoskin Type: Prerequisites: Suitability: A quantum heat engine is a heat engine with a quantum coherent working body.

There exist quantum analogs to classical engine cycles (e.g., Carnot and Otto). You will develop a numerical simulator of a quantum heat engine, which will take into account the processes of decoherence and relaxation and the finite operation speed.

63. Title: Quantum optical effects in a qubit medium Supervisor: Dr A Zagoskin Type: Prerequisites: Suitability: A large array of quantum bits represents a novel type of an optical medium, which is

quantum coherent and locally controllable. You will investigate quantum optical effects (e.g., lasing) in such a medium.