emergence, complexite, universalite des systemes … · emergence, complexite, universalite des...
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EMERGENCE, COMPLEXITE, UNIVERSALITE des SYSTEMES a N CORPS:NOYAUX, ATOMES FROIDS, AGREGATS METALLIQUES, MOLECULES, ...
P. Schuck
IPNO
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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
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MEAN FIELD APPROACHAbout 250 Skyrme forces and nuclear EDF’s !!Stone et al
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In any case quantal fluctuations have to be included: Tselyaev:
New parameter fit!! Very large program!!
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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.
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GW approach to surface of a solid.
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Applications of RPA to molecules.
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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
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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!
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α – Particles Only Exist in Low DensityBEC Phase
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Quartetting
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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
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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!!
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THANK YOU !