On the asymptotic number of edge states for magnetic Schrödinger operators

On the Asymptotic Number of Edge States for Magnetic Schrödinger Operators

We consider a Schrödinger operator (hD−A) with a positive magnetic field B = curlA in a domain Ω ⊂ R. The imposing of Neumann boundary conditions leads to spectrum below h inf B. This is a boundary effect and it is related to the existence of edge states of the system. We show that the number of these eigenvalues, in the semi-classical limit h → 0, is governed by a Weyl-type law and that it inv...

Edge currents and eigenvalue estimates for magnetic barrier Schrödinger operators

We study two-dimensional magnetic Schrödinger operators with a magnetic field that is equal to b > 0 for x > 0 and −b for x < 0. This magnetic Schrödinger operator exhibits a magnetic barrier at x = 0. The unperturbed system is invariant with respect to translations in the ydirection. As a result, the Schrödinger operator admits a direct integral decomposition. We analyze the band functions of ...

Locating the Spectrum for Magnetic Dirac and Schrödinger Operators

“the effect of risk aversion on the demand for life insurance: the case of iranian life insurance market”

abstract: about 60% of total premium of insurance industry is pertained?to life policies in the world; while the life insurance total premium in iran is less than 6% of total premium in insurance industry in 2008 (sigma, no 3/2009). among the reasons that discourage the life insurance industry is the problem of adverse selection. adverse selection theory describes a situation where the inf...

Asymptotics and Gaps in the Spectra of Magnetic Schrödinger Operators

In this paper, we study an L version of the semiclassical approximation of magnetic Schrödinger operators with invariant Morse type potentials on covering spaces of compact manifolds. In particular, we are able to establish the existence of an arbitrary large number of gaps in the spectrum of these operators, in the semiclassical limit as the coupling constant μ goes to zero.