Magnetic Schrödinger operator with the potential supported in a curved two-dimensional strip

2023/08/27 by Reyes, Juan Bory, Schneider, Baruch, Schneiderova, Diana · 1 citation
#FOS: Mathematics #Functional Analysis (math.FA) #Spectral Theory (math.SP)

paper · doi:10.48550/arxiv.2308.14200

Abstract

We consider the magnetic Schrödinger operator H=(i ∇ +A)²- V with a non-negative potential V supported over a strip which is a local deformation of a straight one, and the magnetic field B:=rot(A) is assumed to be nonzero and local. We show that the magnetic field does not change the essential spectrum of this system, and investigate a sufficient condition for the discrete spectrum of H to be empty.

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