Molecular dynamics simulation of strongly coupled QCD plasmas Peter Hartmann 1 Molecular dynamics simulation of strongly coupled QCD plasmas Péter Hartmann

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Peter Hartmann <[email protected]> 1

Molecular dynamics simulation of strongly coupled QCD plasmas

Péter Hartmann1

Zoltán Donkó1

Gabor J. Kalman2

Péter Lévai3

1 Research Institute for Solid State Physics and Optics of the Hungarian Academy of Sciences

H-1525 Budapest, P.O. Box 49Hungary

2 Department of Physics, Boston CollegeChestnut Hill, MA 02467

USA

3 KFKI Research Institute for Particle and Nuclear Physics H-1525 Budapest, P.O. Box 49

Hungary

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Molecular dynamics simulation of strongly coupled QCD plasmas

● Introduction– strongly interacting quark-gluon plasma

– classical, strongly coupled, abelian plasmas

● The molecular dynamics simulation

– potential model for QCD forces – color rotation (random gluon interaction)

● Results of the simulation– resonant plasma heating

– clusterization, correlation

● Results of the model

– plasma coupling parameter

Outline

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Introduction – The quark-gluon plasma Lattice QCD (Fodor, Katz; JHEP 040 (2004) 050):

The aim of this work is to apply classical strongly coupled plasma physics methods

to describe sQGP properties.

Latest results:

• Cross-over phase transition• Strongly correlated

(liquid-like) system• Massive quasi particles

Similar properties to classical, strongly interactingabelian plasma (with large )

sQGP

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electronbackground

ions

Introduction – classical strongly coupled plasmas

The simplest system: classical one-component plasma (OCP).

OCP: charged heavy particles immersed into a homogeneous neutralizing background.

system parameters:

particle density n

particle mass melectric charge QTemperature T

plasma coupling parameter

ion sphere radius

plasma frequency

3 43 naWS

TkaQ BWS2

mnQp2 4

universal parameters:

r

QrV

2

)( interaction (Coulomb) potential:

investigated properties:

• structure (pair correlation function, static structure function)• thermodynamics (internal energy, compressibility, equation of state, phase diagram)• transport phenomena (thermal conductivity, shear viscosity, diffusion)• collective dynamics (density and current fluctuations, dispersion relations, instabilities)

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Our modelOur sQGP model is rooted on the classical OCP model. The links are:

ijij r

QrV

2

)( ij

Sji

ij rrV

)(

Tka

Q

BWS

2

classical OCP QGP model

ions quarks (massive)

electron background(neutralizing)

gluon background(interacting !!!)

Tka

C

BWS

S

The numerical simulation is based on the classical molecular dynamics scheme:

• calculating the forces acting on each particle due to all other particles • integrating the equation of motion for all particles in each time-step• using periodic boundary conditions to handle long range forces• implementing color rotation due to random gluonic interaction

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potential model for QCD interaction

color dependent interaction potential between quark i and j:

possible two-quark states ( R, G and B are the single-quark color states):

color factor:+1/3 symmetric (6)

- 2/3 antisymmetric (3)

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The interaction matrixConsequences: • equally colored quarks repulse each other

• different colors may repulse or attract each other

An example:

interaction matrix of a 9-quark system (excluding self-interaction and double counting)

where D =+1/3 with 50% prob.

- 2/3 with 50% prob.

quark-gluon interaction:

• redistribution of elements D in the interaction matrix (with a characteristic

time: D)

• “color rotation”: exchange of colors of

some quark pairs (C)

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MD results

In the following we present preliminary molecular dynamics results for quark plasma with physical parameters:

• kinetic temperature, T0 = 200 MeV

• particle density, n = 10 quarks / fm3

• interaction strength, S = 1

• quark mass, m = 300 MeV

and technical parameters:

• number of particles, N = 300 • starting positions = random

• initialization time, ti = 106+1 dt

• measure time, tm = 2x105 dt

• time-step, dt = 5x10-5 fm

• cutoff distance, rcut= 0.1 fm

measured parameters are:

• kinetic temperature, T(t) • pair correlation function, g(r)

0

1

1

1

0

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Resonant plasma heating

0 1 2 3 4 5

200

400

600

800

1000

1200

1400

1600

1800

2000 D

tem

pe

ratu

re [

Me

V]

time [fm/c]

1.7 fm/c 0.5 fm/c 0.17 fm/c 0.05 fm/c 0.017 fm/c 0.005 fm/c 0.0017 fm/c

no change

Increase of system temperature

appears due to the redistribution

of the interparticle forces

(reassignment of D terms):

0,01 0,1 1 100

200400600800

100012001400160018002000

tem

pe

ratu

re [

Me

V]

D [fm/c]

t = 1 fm/c t = 2 fm/c t = 4 fm/c

Heating rate depends on D

p

and the colorrotation rate:

0.01 0.1 1 100

200400600800

1000120014001600180020002200 t = 4 fm/c

tem

pe

ratu

re [

Me

V]

D [fm/c]

NC = 0 %

NC = 50 %

NC = 100 %

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Clusterization

0,01 0,1 1 10

400

800

1200

1600

2000

tem

pe

ratu

re [

Me

V]

D [fm/c]

p t=4 fm/c

0

1

1

1

0

0

1

1

1

0

The structural evolution of the

system is determined

by the time dependence of the

interaction (& color rotation) :

0,0 0,5 1,00,0

0,5

1,0

y/L

x/L

0

1

1

1

0

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0 1 2 3 40.0

0.5

1.0

1.5OCP

= 20liquid

g(r

)

r/aWS

0 1 2 3 40.0

1.0

2.0

3.0 OCP = 200solid

g(r

)

r/aWS

0 1 2 3 40.0

0.5

1.0OCP

= 2gas

g(r

)

r/aWS

Correlations

0.0 0.5 1.0 1.5 2.0 2.5 3.00.0

0.5

1.0

1.5

2.0

2.5

3.0

T = 200 MeV

n = 10 q/fm3

m = 300 MeV = 1

D = 0.0005 fm

all particles different colors equal colors

g(r)

r/aWS

0 1 2 3 40.0

0.5

1.0

3x g

(r)

/equ

al c

olor

s/

r/aWS

More detailed insight into

structural properties gives the

pair-correlation function – g(r):

Using g(r) data solid, liquid and

gas structural phases can be

identified.

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0 5 10 15 20

0,2

0,4

0,6

0,8

1,0

1,2

1,4

T = 200 MeV = 1

n [ fm -3 ]

200 400 600 800 1000

0,2

0,4

0,6

0,8

1,0

1,2

1,4

T [ MeV ]

n = 10 fm-3

= 1

0,0 0,5 1,0 1,5 2,0 2,5 3,00

1

2

3

T = 200 MeV

n = 10 fm-3

The plasma coupling parameter - What is the value of for the quark plasma?

rr

erV E

11

4)(

0

2

ES 137

KE

PE

Tka BWS

E

OCP [in SI units] quark plasma

Tka

C

BWS

S

rrV

ji

S

)(

default parameters: n = 10 fm-3, T = 200 MeV, S= 1, C = 1/3 = 1.15

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Summary

Discussions with Miklos Gyulassy and the support by grants OTKA T-48389, MTA-OTKA-90/46140, NSF-PHYS-0206695 and DOE-DE-FG02-03ER5471 are gratefully acknowledged.

• We have presented a possible application of the methodology developed for

strongly coupled EM plasmas for the numerical investigation of sQGP.

• A quasi-classical implementation of the QCD interaction has been developed.

• Simulations were carried out for quark plasma near the critical temperature

• energy transfer from the background filed shows a resonance like

behavior

• structural studies show the tendency of cluster formation

• pair correlation functions show the presence of short-range correlations

• the plasma coupling parameter is in the order of unityTo do:

Lots of exciting research

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Thank youfor your attention!

Documents

Molecular dynamics simulation of strongly coupled QCD plasmas Peter Hartmann 1 Molecular dynamics simulation of strongly coupled QCD plasmas Péter Hartmann