Author(s):

Frank, Rupert L; Hainzl, Christian; Schlein, Benjamin; Seiringer, Robert

Article Title: 
Incompatibility of timedependent Bogoliubov–deGennes and Ginzburg–Landau equations

Affiliation 
IST Austria 
Abstract: 
We study the timedependent Bogoliubov–deGennes equations for generic translationinvariant fermionic manybody 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 timedependent Ginzburg–Landau equation, which is often employed as a phenomenological description and predicts a decay of the order parameter in time. The full nonlinear structure of the equations is necessary to understand this behavior.

Keywords: 
critical temperature; Quasifree states; Superconductivity; BCS theory

Journal Title:

Letters in Mathematical Physics

Volume: 
106

Issue 
7

ISSN:

15730530

Publisher:

Springer

Date Published:

20160701

Start Page: 
913

End Page:

923

Copyright Statement: 
CC BY 4.0

URL: 

DOI: 
10.1007/s1100501608475

Notes: 
Open access funding provided by Institute of Science and Technology (IST Austria). Financial support from the U.S. National Science Foundation through Grants PHY1347399 and DMS1363432 (R.L.F.), SwissMAP and SNF Grant Nr.200021153621 (B.S.), and the Austrian Science Fund (FWF) project Nr. P 27533N27 (R.S.) is acknowledged.

Open access: 
yes (OA journal) 