Asymptotic of the density of states for the Schrödinger operator with periodic electromagnetic potential

DOI10.1063/1.532105zbMath0883.47045OpenAlexW2020134704MaRDI QIDQ4351632

Arbderemane Mohamed

Publication date: 11 November 1997

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1063/1.532105

zbMATH Keywords

integrated density of statesasymptotic formulaBethe-Sommerfeld conjecture

Mathematics Subject Classification ID

General topics in linear spectral theory for PDEs (35P05) General theory of partial differential operators (47F05) Schrödinger operator, Schrödinger equation (35J10)

Related Items (16)

Bethe–Sommerfeld Conjecture for Pseudodifferential Perturbation ⋮ On lacunas in the lower part of the spectrum of the periodic magnetic operator in a strip ⋮ On the Bethe-Sommerfeld conjecture for certain periodic Maxwell operators ⋮ Complete asymptotic expansion of the integrated density of states of multidimensional almost-periodic pseudo-differential operators ⋮ On spectral gaps of a Laplacian in a strip with a bounded periodic perturbation ⋮ Asymptotic of the density of states for the Schrödinger operator with periodic electric potential ⋮ THE BETHE–SOMMERFELD CONJECTURE FOR THE 3-DIMENSIONAL PERIODIC LANDAU OPERATOR ⋮ Spectral properties of the periodic magnetic Schrödinger operator in the high-energy region. Two-dimensional case ⋮ Microlocal analysis of the bulk-edge correspondence ⋮ Bethe-Sommerfeld conjecture for periodic operators with strong perturbations ⋮ Gaps in the spectrum of the Laplacian in a strip with periodic delta interaction ⋮ Absence of gaps in a lower part of the spectrum of a Laplacian with frequent alternation of boundary conditions in a strip ⋮ An overview of periodic elliptic operators ⋮ On lacunas in the spectrum of the Laplacian with the Dirichlet boundary condition in a band with oscillating boundary ⋮ On the density of states for the periodic Schrödinger operator ⋮ Bethe-Sommerfeld conjecture for periodic Schrödinger operators in strip

Cites Work

• A remark on two dimensional periodic potentials
• Characterization of pseudodifferential operator and application
• Strong magnetic fields, Dirichlet boundaries, and spectral gaps
• Semiclassical analysis for the ground state energy of a Schrödinger operator with magnetic wells
• The spectral function of an elliptic operator

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