Global-in-time semiclassical regularity for the Hartree–Fock equation-Reference-Cited by-同舟云学术

Global-in-time semiclassical regularity for the Hartree–Fock equation

Published:2022-08-01 Issue:8 Volume:63 Page:081904
ISSN:0022-2488
Container-title:Journal of Mathematical Physics
language:en
Short-container-title:J. Math. Phys.

Author:

Chong J. J.¹^ORCID,Lafleche L.¹^ORCID,Saffirio C.²^ORCID

Affiliation:

1. Department of Mathematics, The University of Texas at Austin, Austin, Texas 78712, USA

2. Department of Mathematics and Computer Science, Spiegelgasse 1, 4051 Basel, Switzerland

Abstract

For arbitrarily large times T > 0, we prove the uniform-in- ℏ propagation of semiclassical regularity for the solutions to the Hartree–Fock equation with singular interactions of the form [Formula: see text] with [Formula: see text]. As a by-product of this result, we extend to arbitrarily long times the derivation of the Hartree–Fock and the Vlasov equations from the many-body dynamics provided in the work of Chong et al. [ arXiv:2103.10946 (2021)].

Funder

Schweizerischer Nationalfonds zur Förderung der Wissenschaftlichen Forschung

Division of Mathematical Sciences

Publisher

AIP Publishing

Subject

Mathematical Physics,Statistical and Nonlinear Physics

Link

https://aip.scitation.org/doi/pdf/10.1063/5.0089741

Reference20 articles.

1. L2 Solutions to the Schrödinger–Poisson System: Existence, Uniqueness, Time Behaviour, and Smoothing Effects

2. On a class of non linear Schr�dinger equations with non local interaction