Related papers: Semiclassical Limit of the Bogoliubov-de Gennes Equation

Semiclassical Limit of the Bogoliubov-de Gennes Equation

URL: http://arxiv.org/abs/2403.15880v1
Date: Sat, 23 Mar 2024 16:19:21 GMT
Title: Semiclassical Limit of the Bogoliubov-de Gennes Equation
Authors: Jacky J. Chong, Laurent Lafleche, Chiara Saffirio,
Abstract summary: We establish a semiclassical and mean-field approximation of the dynamics of a system spin-$frac2$ Fermions by the Vlasov equation. For some semiclassical regimes, we obtain a higher-order correction to the twoparticle kinetic transport equation.
Score: 0.0
License: http://creativecommons.org/licenses/by/4.0/
Abstract: In this paper, we rewrite the time-dependent Bogoliubov$\unicode{x2013}$de Gennes equation in an appropriate semiclassical form and establish its semiclassical limit to a two-particle kinetic transport equation with an effective mean-field background potential satisfying the one-particle Vlasov equation. Moreover, for some semiclassical regimes, we obtain a higher-order correction to the two-particle kinetic transport equation, capturing a nontrivial two-body interaction effect. The convergence is proven for $C^2$ interaction potentials in terms of a semiclassical optimal transport pseudo-metric. Furthermore, combining our current results with the results of Marcantoni et al. [arXiv:2310.15280], we establish a joint semiclassical and mean-field approximation of the dynamics of a system of spin-$\frac{1}{2}$ Fermions by the Vlasov equation in some negative order Sobolev topology.

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