Tunisian Journal of Mathematics

Semiclassical approximation of the magnetic Schrödinger operator on a strip: dynamics and spectrum

Mouez Dimassi

Abstract

In the semiclassical regime (i.e., $ϵ↘0$), we study the effect of a slowly varying potential $V(ϵt,ϵz)$ on the magnetic Schrödinger operator $P=Dx2+(Dz+μx)2$ on a strip $[−a,a]×ℝz$. The potential $V(t,z)$ is assumed to be smooth. We derive the semiclassical dynamics and we describe the asymptotic structure of the spectrum and the resonances of the operator $P+V(ϵt,ϵz)$ for $ϵ$ small enough. All our results depend on the eigenvalues corresponding to $Dx2+(μx+k)2$ on $L2([−a,a])$ with Dirichlet boundary condition.

Article information

Source
Tunisian J. Math., Volume 2, Number 1 (2020), 197-215.

Dates
Revised: 17 November 2018
Accepted: 2 December 2018
First available in Project Euclid: 2 April 2019

https://projecteuclid.org/euclid.tunis/1554170465

Digital Object Identifier
doi:10.2140/tunis.2020.2.197

Mathematical Reviews number (MathSciNet)
MR3933395

Zentralblatt MATH identifier
07074074

Citation

Dimassi, Mouez. Semiclassical approximation of the magnetic Schrödinger operator on a strip: dynamics and spectrum. Tunisian J. Math. 2 (2020), no. 1, 197--215. doi:10.2140/tunis.2020.2.197. https://projecteuclid.org/euclid.tunis/1554170465

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