Incompatibility of time-dependent Bogoliubov--de-Gennes and Ginzburg--Landau equations

Abstract

We study the time-dependent Bogoliubov--de-Gennes equations for generic translation-invariant fermionic many-body systems. For initial states that are close to thermal equilibrium states at temperatures near the critical temperature, we show that the magnitude of the order parameter stays approximately constant in time and, in particular, does not follow a time-dependent Ginzburg--Landau equation, which is often employed as a phenomenological description and predicts a decay of the order parameter in time. The full non-linear structure of the equations is necessary to understand this behavior.

to appear in LMP

References in corpus (4)

• Critical Temperature and Energy Gap for the BCS Equation
• The BCS Functional for General Pair Interactions
• Multi-component Ginzburg-Landau theory: microscopic derivation and examples
• The external field dependence of the BCS critical temperature

Cited by in corpus (9)

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• General pairing mechanisms in the BCS-theory of superconductivity
• Quenched dynamics and pattern formation in clean and disordered Bogoliubov-de Gennes superconductors
• The Meissner effect in superconductors: emergence versus reductionism
• A lower bound for the BCS functional with boundary conditions at infinity
• Dynamics of mean-field Fermi systems with nonzero pairing
• A splitting integrator for the BCS equations of superconductivity
• Enhanced pairing mechanism in Cuprate-type crystals
• Differential Equations of Quantum Mechanics