Local spectral asymptotics for metric perturbations of the Landau Hamiltonian

Lungenstrass, Tomás; Raikov, Georgi

doi:10.2140/apde.2015.8.1237

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Local spectral asymptotics for metric perturbations of the Landau Hamiltonian

Tomás Lungenstrass and Georgi Raikov

Vol. 8 (2015), No. 5, 1237–1262

DOI: 10.2140/apde.2015.8.1237

Abstract

We consider metric perturbations of the Landau Hamiltonian. We investigate the asymptotic behavior of the discrete spectrum of the perturbed operator near the Landau levels, for perturbations of compact support, and of exponential or power-like decay at infinity.

Keywords

Landau Hamiltonian, metric perturbations, position-dependent mass, spectral asymptotics

Mathematical Subject Classification 2010

Primary: 35J10, 35P20, 47G30, 81Q10

Milestones

Received: 3 December 2014

Revised: 30 January 2015

Accepted: 15 April 2015

Published: 28 July 2015

Authors

Tomás Lungenstrass
Facultad de Matemáticas Pontificia Universidad Católica de Chile Vicuña Mackenna 4860 7820436 Santiago Chile

Georgi Raikov
Facultad de Matemáticas Pontificia Universidad Católica de Chile Vicuña Mackenna 4860 7820436 Santiago Chile

Vol. 8, No. 5, 2015