-

EMERGENCE, COMPLEXITE, UNIVERSALITE des SYSTEMES a N CORPS:NOYAUX, ATOMES FROIDS, AGREGATS METALLIQUES, MOLECULES, ...

P. Schuck

IPNO

CONTENT

Nuclear Mean Field: dead end.

Inclusion of quantal fluctuations and more correlations

Second RPA; Coupled Cluster; TDDM.

Overlap with Chemistry

Overlap with Cold Atoms

Overlap with small metallic clusters

Conclusions

MEAN FIELD APPROACHAbout 250 Skyrme forces and nuclear EDF’s !!Stone et al

In any case quantal fluctuations have to be included: Tselyaev:

New parameter fit!! Very large program!!

10 15 20 25 30E (MeV)

0

2

4

6

8

B(E

0)

(e2fm

4M

eV

-1)

SRPASSRPA

D

SSRPAF

Second RPA with substraction; monopole spectrum, M. Grasso et al.

GW approach to surface of a solid.

Applications of RPA to molecules.

Pairing in neutron matterVery long nn s-wave scattering length: anns ∼ -18 fm; at low density almost coldatom conditions!

0 0.1 0.2 0.3 0.4 0.5 0.6

kF [fm

-1]

0

0.5

1

1.5

2

2.5

∆ (

MeV

)

BCSChen 93Wambach 93Schulze 96Schwenk 03Fabrocini 05Cao 06dQMC 09

AFDMC 08QMC AV4

0 2 4 6 8 10 12- k

F a

Coupled Cluster Theory (CCT) Applications in Chemistry and nuclei

0.75

0.8

0.85

0.9

0.95

1

1.05

1.1

0 0.1 0.2 0.3 0.4 0.5 0.6

Ec

/ E

cexac

t

G / ∆ε

Gc

BCS p-CCDBCS p-BCCDPBCS

False first order phase transition!

α – Particles Only Exist in Low DensityBEC Phase

Quartetting

0 1 2 3 410-4

10-3

10-2

10-1

k (fm-1)

f pt(

k)

VMC

GFMC

Experiment

0 0.2 0.40

1

2

3

4

5

6

k2 (fm-2)

6 Z

ftr

(k)

/ k2

(

fm2)

LEFT: THSR result; no adjustable parameter; ρ = ρ0/3

RIGHT: GFMC result (R. Wiringa, Pieper, .., RMP); no afjustable parameter

Self-Consistent RPA ↔ Time Dependent Density MatrixTohyama, P. Sch.

i ρ = [hHF, ρ] + vC2

i C2 = ...ρ,C2+ v [C3 ∼ C2 ⊗ C2]

Standard RPA: ground state: Slater;( C2 = 0)

S0χ0 = Ω0Nχ0

Inclusion of C2: → Second RPA: ground state: CCD(S BB+ D

)(χ1

X2

)= Ω

(N TT + N2

)(χ1

X2

)(1)

Self-Consistent RPA:

S [χ1]χ1 = ΩNχ1

SCRPA: all properties like RPA! Goldstone, Ward identities, etcKadanoff-Baym → dead end! Too complicated!!

THANK YOU !