Concentration of Bloch eigenstates in the presence of gauge at the semi-classical limit

DOI10.1016/S0252-9602(11)60399-8zbMATH Open1265.35232arXiv0902.3355OpenAlexW2151012022MaRDI QIDQ453394

Gershon Wolansky

Publication date: 5 October 2012

Published in: Acta Mathematica Scientia. Series B. (English Edition) (Search for Journal in Brave)

Abstract: We prove a concentration result of a Bloch eigenstate in a periodic channel under a constant gauge. In the semi-classical limit $h-->0$ these eigenstates concentrate near a maximizer of the scalar potential of the associated Schrodinger operator, provided the constant gauge converges to a critical value from above. This is in contrast with the ground states which concentrate for any gauge in this limit near a minimizer of the scalar potential.

Full work available at URL: https://arxiv.org/abs/0902.3355

zbMATH Keywords

Schrödinger equationsemi-classical limitgaugeBloch eigenstate

Mathematics Subject Classification ID

General topics in linear spectral theory for PDEs (35P05) Schrödinger operator, Schrödinger equation (35J10) Perturbation theories for operators and differential equations in quantum theory (81Q15)

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