Asymptotic distribution of negative eigen values for two dimensional Pauli operators with spherically symmetric magnetic fields

Asymptotic distribution of negative eigenvalues for two dimensional Pauli operators with nonconstant magnetic fields

On the spectrum of two-dimensional Schrödinger operators with spherically symmetric, radially periodic magnetic fields

We investigate the spectrum of the two-dimensional Schrödinger operator H = @ @x ia1(x; y) 2 @ @y ia2(x; y) 2 + V (x; y), where the magnetic field B(x; y) = @ @x a2 @ @y a1 and the electric potential V are spherically symmetric, i.e., B(x; y) = b(r), r = px2 + y2, and b is p-periodic, similarly for V . By considering two different gauges we get the following results: In case R p 0 b(s) ds = 0 t...

Asymptotic Distribution of Eigenvalues for Pauli Operators with Nonconstant Magnetic Fields

Low Energy Asymptotics of the SSF for Pauli Operators with Nonconstant Magnetic Fields

We consider the 3D Pauli operator with nonconstant magnetic field B of constant direction, perturbed by a symmetric matrix-valued electric potential V whose coefficients decay fast enough at infinity. We investigate the low-energy asymptotics of the corresponding spectral shift function. As a corollary, for generic negative V , we obtain a generalized Levinson formula, relating the low-energy a...

The Negative Discrete Spectrum of a Class of Two–Dimentional Schrödinger Operators with Magnetic Fields

We obtain an asymptotic formula for the number of negative eigenvalues of a class of two-dimensional Schrödinger operators with small magnetic fields. This number increases as a coupling constant of the magnetic field tends to zero. 1.Introduction and Notations. Let us consider a selfadjoint Schrödinger operator in L(R) formally written as (1.1) Hβ = (i∇+ βA) − V, β > 0. Here the electric poten...