Magnetic bottles on the Poincar\'e half-plane: spectral asymptotics

TL;DR

This paper studies the spectral properties of a magnetic Laplacian on the Poincaré half-plane with an infinite magnetic field, deriving the asymptotic behavior of its eigenvalue counting function.

Contribution

It provides the first detailed spectral asymptotics for the magnetic Laplacian in this geometric setting with an unbounded magnetic field.

Findings

Eigenvalue counting function asymptotics derived

Spectral behavior characterized for infinite magnetic field

Mathematical framework established for spectral analysis

Abstract

We consider a magnetic laplacian P(A) on the Poincar\'e half-plane, when the magnetic field dA is infinite at infinity such that P(A) has pure discret spectrum. We give the asymptotic behavior of the counting function of the eigenvalues.