Semiclassical analysis of the magnetic Laplacian on hyperbolic surfaces
Thibault Lefeuvre
TL;DR
This paper provides a concise overview of the semiclassical analysis of the magnetic Laplacian on hyperbolic surfaces, highlighting quantum phenomena and recent research developments in this mathematical physics area.
Contribution
It summarizes recent results and ongoing work on the spectral properties of the magnetic Laplacian in hyperbolic geometry, emphasizing new analytical insights.
Findings
Characterization of spectral properties of the magnetic Laplacian
Identification of quantum phenomena in hyperbolic surfaces
Summary of recent advances in semiclassical analysis
Abstract
The magnetic Laplacian on hyperbolic surfaces provides a rich analytic framework in which a variety of quantum phenomena emerge. The present note, written for the \emph{Proceedings of the Journ\'ees EDP 2025}, is a concise overview of the main results obtained in [arXiv:2505.08584] and work in preparation by the author with L. Charles and A. Chabert.
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Taxonomy
TopicsSpectral Theory in Mathematical Physics · Quantum chaos and dynamical systems · Mathematical Dynamics and Fractals