Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1504.05881 · The European Physical Journal B

Comparing the full time-dependent Bogoliubov-de-Gennes equations to their linear approximation: a numerical investigation

Christian Hainzl, Jonathan Seyrich

Published May 1, 2016• 10 citations
arXivHTMLPDF
DOI
10.1140/epjb/e2016-60975-y

Related papers

Discretization and solution of the inhomogeneous Bogoliubov–de Gennes equations

Dermot McPeake, J F McCann

Computer Physics Communications•Jul 20, 2004•5 citations

Bogoliubov de Gennes equation using lattice Boltzmann model

F. Fonseca

Advanced Studies in Theoretical Physics•Jan 1, 2016•0 citations

Time-dependent Bogoliubov equations

John B. Ketterson, Shenian N. Song

Cambridge University Press eBooks•Jan 12, 1999•0 citations

Comparing the full time-dependent BCS equation to its linear approximation: A numerical investigation

Christian Hainzl, Jonathan Seyrich

In this paper we report on the results of a numerical study of the nonlinear time-dependent Bardeen--Cooper--Schrieffer (BCS) equation, often also denoted as Bogoliubov--de--Gennes (BdG) equation, for a one-dimensional system of fermions with contact interaction. We show that the full equation and its linear approximation give rise to completely different evolutions. This strongly contradicts the existence of a diffusive nonlinear time-dependent Ginzburg--Landau equation, in accordance with a recent theoretical result by Frank, Hainzl, Schlein, and Seiringer. We include a full description on the numerical implementation of the partial differential equations.

•Apr 22, 2015•2 citations

Incompatibility of Time-Dependent Bogoliubov–de-Gennes and Ginzburg–Landau Equations

Rupert L. Frank, Christian Hainzl, Benjamin Schlein +1 more

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.

arXiv:1504.05885•Letters in Mathematical Physics•May 10, 2016•11 citations

A new method for solving the inhomogeneous Bogoliubov - de Gennes equations

Lucian Covaci, Mona Berciu

Bulletin of the American Physical Society•Mar 19, 2009•0 citations
In this paper we report on the results of a numerical study of the nonlinear time-dependent Bardeen--Cooper--Schrieffer (BCS) equation, often also denoted as Bogoliubov--de--Gennes (BdG) equation, for a one-dimensional system of fermions with contact interaction. We show that the full equation and its linear approximation give rise to completely different evolutions. This strongly contradicts the existence of a diffusive nonlinear time-dependent Ginzburg--Landau equation, in accordance with a recent theoretical result by Frank, Hainzl, Schlein, and Seiringer. We include a full description on the numerical implementation of the partial differential equations.
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.