Mean-Field Regime for Fermionic Systems

AbstractWe study the time dependent Schrödinger equation for large spinless fermions with the semiclassical scale $$\hbar = N^{-1/3}$$ ħ = N - 1 / 3 in three dimensions. By using the Husimi measure defined by coherent states, we rewrite the Schrödinger equation into a BBGKY type of hierarchy for the k particle Husimi measure. Further estimates are derived to obtain the weak compactness of the Husimi measure, and in addition uniform estimates for the remainder terms in the hierarchy are derived in order to show that in the semiclassical regime the weak limit of the Husimi measure is exactly the solution of the Vlasov equation.

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Two-term expansion of the ground state one-body density matrix of a mean-field Bose gas

Calculus of Variations and Partial Differential Equations ◽

10.1007/s00526-021-01954-2 ◽

2021 ◽

Vol 60 (3) ◽

Author(s):

Phan Thành Nam ◽

Marcin Napiórkowski

Keyword(s):

Density Matrix ◽

Ground State ◽

Mean Field ◽

Interaction Strength ◽

Bose Gas ◽

Body Density ◽

The Mean ◽

The One ◽

Mean Field Regime ◽

Number Of Particles

AbstractWe consider the homogeneous Bose gas on a unit torus in the mean-field regime when the interaction strength is proportional to the inverse of the particle number. In the limit when the number of particles becomes large, we derive a two-term expansion of the one-body density matrix of the ground state. The proof is based on a cubic correction to Bogoliubov’s approximation of the ground state energy and the ground state.

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Mean-Field Regime for Bosonic Systems

Effective Evolution Equations from Quantum Dynamics - SpringerBriefs in Mathematical Physics ◽

10.1007/978-3-319-24898-1_2 ◽

2015 ◽

pp. 7-16 ◽

Cited By ~ 1

Author(s):

Niels Benedikter ◽

Marcello Porta ◽

Benjamin Schlein

Keyword(s):

Mean Field ◽

Mean Field Regime

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A RENORMALIZATION GROUP APPROACH FOR MANY-FERMION PROBLEMS

International Journal of Modern Physics B ◽

10.1142/s021797929200044x ◽

1992 ◽

Vol 06 (05n06) ◽

pp. 749-758 ◽

Cited By ~ 3

Author(s):

R. SHANKAR

Keyword(s):

Renormalization Group ◽

Landau Theory ◽

Mean Field Theory ◽

Mean Field ◽

Free Fermion ◽

Fermion System ◽

Group Approach ◽

Fermionic Systems ◽

Renormalization Group Approach ◽

The Stability

A renormalization group transformation (RGT) that permits us to analyze the stability of fermionic systems to various perturbations in any number of dimensions is developed. An RGT that leaves invariant the free fermion system (on or off a lattiice) is defined and interactions are classified as relevent, irrelevent or marginal. It is shown how the RGT automatically considers competing instabilities simultaneously, in contrast to mean field theory, which focuses on just one. It is shown that at weak coupling only the BCS coupling is relevent unless there is nesting. Both Landau theory and the Kohn-Luttinger argument are discussed in this context.

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FLUCTUATION CONDUCTIVITY EFFECTS ON THERMOELECTRIC POWER OF GRANULAR Bi1.75Pb0.25Ca2Sr2Cu3O10 SUPERCONDUCTOR

Modern Physics Letters B ◽

10.1142/s0217984989000406 ◽

1989 ◽

Vol 03 (03) ◽

pp. 241-248 ◽

Cited By ~ 29

Author(s):

CH. LAURENT ◽

S.K. PATAPIS ◽

S.M. GREEN ◽

H.L. LUO ◽

C. POLITIS ◽

...

Keyword(s):

Electrical Resistivity ◽

High Temperature ◽

Thermoelectric Power ◽

High Temperature Superconductivity ◽

Mean Field ◽

Temperature Derivative ◽

Fluctuation Conductivity ◽

Straight Line ◽

The Mean ◽

Mean Field Regime

We report precise measurements of the thermoelectric power (TEP) of granular superconducting Bi 1.75 Pb 0.25 Ca 2 Sr 2 Cu 3 O 10. The TEP is strictly linear at high temperature. Superconductivity fluctuations set in at about 140 K. From the temperature derivative of the excess TEP (with respect to a straight line at “high temperature”), the critical behavior is obtained in the mean field regime, and is found identical to that of the temperature derivative of the excess electrical resistivity.

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Mean–Field Evolution of Fermionic Systems

Communications in Mathematical Physics ◽

10.1007/s00220-014-2031-z ◽

2014 ◽

Vol 331 (3) ◽

pp. 1087-1131 ◽

Cited By ~ 40

Author(s):

Niels Benedikter ◽

Marcello Porta ◽

Benjamin Schlein

Keyword(s):

Mean Field ◽

Field Evolution ◽

Fermionic Systems

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EXCESS CONDUCTIVITY IN THE MEAN FIELD AND PARACOHERENCE REGIMES OF (La1.6Y0.4)Ba2Ca0.8Cu4.8Oz SUPERCONDUCTORS

Modern Physics Letters B ◽

10.1142/s0217984906009499 ◽

2006 ◽

Vol 20 (02n03) ◽

pp. 111-122 ◽

Cited By ~ 1

Author(s):

P. K. NAYAK ◽

S. RAVI

Keyword(s):

Heisenberg Model ◽

Order Parameter ◽

Mean Field ◽

Excess Conductivity ◽

Temperature Variations ◽

Phase Fluctuations ◽

Higher Temperature ◽

The Mean ◽

Breaking Time ◽

Mean Field Regime

The temperature variations of electrical resistivity have been measured on pure and 5 wt% Ag doped ( La 1.6 Y 0.4) Ba 2 Ca 0.8 Cu 4.8 O z superconductors. These data were analyzed in terms of fluctuation-induced excess conductivity in the mean field regime by using the Aslamazov–Larkin (AL), Lawrence–Doniach (LD) and Maki–Thompson (MT) models. The fluctuations in the amplitude of order parameter are found to be two dimensional in nature in the mean field region. The estimated values of the average phase breaking time τϕ (100 K) are found to be 3.9×10-16 s and 4.6×10-16 s for pure and Ag doped samples respectively. The resistivity data were also analyzed in terms of excess conductivity due to phase fluctuations of the order parameter in the paracoherence region. The critical exponent is found to be mostly comparable to that of the 3D XY ferromagnet in the vicinity of zero resistivity temperature and the diluted Heisenberg model at a higher temperature.

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