Book contents
- Frontmatter
- Dedication
- Contents
- Author’s Note
- Part INormal Phase
- Part IIFermionic Superfluid Phase
- 21Time-Dependent BCS Hamiltonian and Gor’kov Equations
- 22The Hamiltonian in the Nambu Representation and the Role of the Hartree–Fock–BCS Self-Energy
- 23Contour-Ordered Green’s Functions in the Nambu Representation
- 24The T-matrix Approximation in the Superfluid Phase
- 25Derivation of the Time-Dependent Bogoliubov–deGennes Equations
- 26A Brief Excursus to the BCS–BEC Crossover
- 27Analytic Continuation from the Imaginary to the Real-Time Axis
- 28Derivation of the Time-Dependent Gross–Pitaevskii Equation for Composite Bosons in the BEC Limit of the BCS–BEC Crossover
- 29Derivation of the Time-Dependent Ginzburg–Landau Equation for Cooper Pairs in the BCS Limit of the BCS–BEC Crossover
- 30Real-Frequency Green’s Functions from the Kadanoff–Baym Equations in the Equilibrium Case
- 31Miscellany and Addenda to Part II
- Part IIIApplications
- Bibliography
- Index
31 - Miscellany and Addenda to Part II
from Part II - Fermionic Superfluid Phase
Published online by Cambridge University Press: 06 February 2026
Book contents
- Frontmatter
- Dedication
- Contents
- Author’s Note
- Part INormal Phase
- Part IIFermionic Superfluid Phase
- 21Time-Dependent BCS Hamiltonian and Gor’kov Equations
- 22The Hamiltonian in the Nambu Representation and the Role of the Hartree–Fock–BCS Self-Energy
- 23Contour-Ordered Green’s Functions in the Nambu Representation
- 24The T-matrix Approximation in the Superfluid Phase
- 25Derivation of the Time-Dependent Bogoliubov–deGennes Equations
- 26A Brief Excursus to the BCS–BEC Crossover
- 27Analytic Continuation from the Imaginary to the Real-Time Axis
- 28Derivation of the Time-Dependent Gross–Pitaevskii Equation for Composite Bosons in the BEC Limit of the BCS–BEC Crossover
- 29Derivation of the Time-Dependent Ginzburg–Landau Equation for Cooper Pairs in the BCS Limit of the BCS–BEC Crossover
- 30Real-Frequency Green’s Functions from the Kadanoff–Baym Equations in the Equilibrium Case
- 31Miscellany and Addenda to Part II
- Part IIIApplications
- Bibliography
- Index
Summary
Similar to Chapter 20 of Part I, this chapter considers the treatment of a few topics, which are relevant to the general purposes of the book but whose inclusion in previous chapters would have diverted the discussion of the main topics of interest therein. Specifically, it considers the Dyson equations for the contour single-particle Green’s function in the Nambu representation, the relative strength of different frequency terms in the derivation of the time-dependent Gross–Pitaevskii equation, the detailed calculation of an integral occurring in the derivation of the time-dependent Ginzburg–Landau equation, the irrelevance of the reference time t₀ for the convolutions entering the Kadanoff–Baym equations at equilibrium, and the average energy of the system expressed in terms of the lesser Green’s function even in nonequilibrium situations.
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- Many-Body Green's Functions for Time-Dependent Problems , pp. 285 - 302Publisher: Cambridge University PressPrint publication year: 2026
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