We use a functional integral formulation to study the finite temperature crossover from cooperative Cooper pairing to independent bound state formation and condensation. We show the inadequacy of mean field results for normal state properties obtained at the saddle point level as the coupling increases. The importance of quantum (temporal) fluctuations is pointed out and an interpolation scheme for ${\mathit{T}}_{\mathit{c}}$ is derived from this point of view. The time-dependent Ginzburg-Landau (TDGL) equation near ${\mathit{T}}_{\mathit{c}}$ is shown to describe a damped mode in the BCS limit, and a propagating one in the Bose limit. A singular point is identified at intermediate coupling where a simple TDGL description fails.We use a functional integral formulation to study the finite temperature crossover from cooperative Cooper pairing to independent bound state formation and condensation. We show the inadequacy of mean field results for normal state properties obtained at the saddle point level as the coupling increases. The importance of quantum (temporal) fluctuations is pointed out and an interpolation scheme for ${\mathit{T}}_{\mathit{c}}$ is derived from this point of view. The time-dependent Ginzburg-Landau (TDGL) equation near ${\mathit{T}}_{\mathit{c}}$ is shown to describe a damped mode in the BCS limit, and a propagating one in the Bose limit. A singular point is identified at intermediate coupling where a simple TDGL description fails.

Physical Review LettersNov 8, 1993861 citations

Derivation of the Time-Dependent Ginzburg–Landau Equation for Cooper Pairs in the BCS Limit of the BCS–BEC Crossover

Giancarlo Calvanese Strinati

This chapter derives the time-dependent Ginzburg–Landau equation from first principles, by relying on the same formal approach that has led to the time-dependent Gross–Pitaevskii equation of Chapter 28. Specifically, the time-dependent Ginzburg–Landau equation holds close to the critical temperature of the initial equilibrium preparation and in the (extreme) BCS limit of the BCS–BEC crossover, when the Cooper pairs are largely overlapping with each other. Care has to be exerted when dealing with the analytic properties in the wave-vector and frequency space of the normal and anomalous particle–particle bubbles.This chapter derives the time-dependent Ginzburg–Landau equation from first principles, by relying on the same formal approach that has led to the time-dependent Gross–Pitaevskii equation of Chapter 28. Specifically, the time-dependent Ginzburg–Landau equation holds close to the critical temperature of the initial equilibrium preparation and in the (extreme) BCS limit of the BCS–BEC crossover, when the Cooper pairs are largely overlapping with each other. Care has to be exerted when dealing with the analytic properties in the wave-vector and frequency space of the normal and anomalous particle–particle bubbles.

Cambridge University Press eBooksFeb 6, 20260 citations

Studies in Time-Dependent Correlation Functions.

G. Yue

Oct 1, 19760 citations

{\mathit{T}}_{\mathit{c}}

is derived from this point of view. The time-dependent Ginzburg-Landau (TDGL) equation near

{\mathit{T}}_{\mathit{c}}

is shown to describe a damped mode in the BCS limit, and a propagating one in the Bose limit. A singular point is identified at intermediate coupling where a simple TDGL description fails.