Incompatibility of time-dependent Bogoliubov-de-Gennes and Ginzburg-Landau equations (Q504230)

This paper deals with the study of the time-dependent Bogoliubov-de Gennes equations in the framework of translation-invariant fermionic many-body systems. Problems of this type arise in the BCS theory of superconductivity and superfluidity. The main contribution in the present paper establishes that a time-dependent Ginzburg-Landau equation cannot be derived from the time-dependent Bogoliubov-de Gennes equations near the critical temperature, in contrast to the static case. A comparison with the linear case is also contained in the present paper.