Fermionic semiclassical Lp estimates
arXiv:2205.00722 · doi:10.1016/j.jfa.2023.110196
Abstract
We generalize the semiclassical Lp estimates of Koch, Tataru and Zworski in the setting of Schr{ö}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.
arXiv comment78 pages
References in corpus (5)
- Noninteracting fermions in a trap and random matrix theory
- Wigner function of noninteracting trapped fermions
- Universal ground state properties of free fermions in a -dimensional trap
- Spectral cluster bounds for orthonormal systems and oscillatory integral operators in Schatten spaces
- Impurities in systems of noninteracting trapped fermions