Magnetic field influence on the discrete spectrum of locally deformed leaky wires

Abstract

We consider magnetic Schrödinger operator $H=(i\nabla +A{)}^2-\alpha {\delta }_{\Gamma }$ with an attractive singular interaction supported by a piecewise smooth curve $\Gamma$ being a local deformation of a straight line. The magnetic field $B$ is supposed to be nonzero and local. We show that the essential spectrum is $[-\frac{1}{4}{\alpha }^2,\infty )$, as for the non-magnetic operator with a straight $\Gamma$, and demonstrate a sufficient condition for the discrete spectrum of $H$ to be empty.

10 pages, no figures

References in corpus (2)

• Little Magnetic Book
• Eigenvalue upper bounds for the magnetic Schroedinger operator