Fermionic semiclassical Lp estimates
Analysis of PDEs
2025-03-21 v2 Mathematical Physics
math.MP
Spectral Theory
Abstract
We generalize the semiclassical Lp estimates of Koch, Tataru and Zworski in the setting of Schr{\"o}dinger operators with confining potentials to density matrices. This is motivated by the problem of the concentration of free fermionic particles in a trapping potential. Our proof relies on semiclassical and many-body tools. As an application, we provide bounds on spectral clusters. We also discuss the optimality of the one-body and many-body bounds through explicit examples of quasimodes.
Keywords
Cite
@article{arxiv.2205.00722,
title = {Fermionic semiclassical Lp estimates},
author = {Ngoc Nhi Nguyen},
journal= {arXiv preprint arXiv:2205.00722},
year = {2025}
}
Comments
78 pages