Improved Berezin-Li-Yau inequalities with magnetic field
Hynek Kovarik, Timo Weidl
TL;DR
This paper improves the Li-Yau inequality for eigenvalue sums of Dirichlet Laplacians on bounded domains when a constant magnetic field is present, providing tighter bounds in this setting.
Contribution
It introduces an enhanced version of the Li-Yau inequality accounting for magnetic fields, advancing spectral bounds for magnetic Laplacians.
Findings
Established an improved eigenvalue sum bound with magnetic field
Demonstrated tighter spectral bounds for magnetic Dirichlet Laplacians
Extended classical inequalities to include magnetic effects
Abstract
In this paper we study the eigenvalue sums of Dirichlet Laplacians on bounded domains. Among our results we establish an improvement of the Li-Yau bound in the presence of a constant magnetic field.
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