Fermionic semiclassical Lp estimates
Ngoc Nhi Nguyen (LMO)
TL;DR
This paper extends semiclassical Lp estimates from Schrödinger operators to density matrices, addressing fermionic particle concentration in traps, and provides bounds on spectral clusters with discussions on their optimality.
Contribution
It introduces a generalization of semiclassical Lp estimates to density matrices, combining semiclassical and many-body techniques for fermionic systems.
Findings
Extended Lp estimates to density matrices for fermions.
Provided bounds on spectral clusters in trapping potentials.
Discussed the optimality of bounds through explicit quasimode examples.
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.
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Taxonomy
TopicsSpectral Theory in Mathematical Physics · Mathematical functions and polynomials · Numerical methods in inverse problems