Semiclassical limit of cubic nonlinear Schr\"odinger equations for mixed states
Analysis of PDEs
2025-10-27 v1 Mathematical Physics
math.MP
Abstract
In this work, we study the semiclassical limit of cubic Nonlinear Schr\"odinger equations for mixed states. We justify the limit to a singular Vlasov equation (in which the force field is proportional to the gradient of the density), for data with finite Sobolev regularity whose velocity profiles satisfy a quantum Penrose stability condition. This latter condition is always satisfied for small data (with a smallness condition independent of the semiclassical parameter) both in the focusing and the defocusing case, and for small perturbations of a large class of physically relevant examples in the defocusing case, such as local Maxwellian-like profiles.
Keywords
Cite
@article{arxiv.2510.21313,
title = {Semiclassical limit of cubic nonlinear Schr\"odinger equations for mixed states},
author = {Daniel Han-Kwan and Frédéric Rousset},
journal= {arXiv preprint arXiv:2510.21313},
year = {2025}
}