Existence and uniqueness of the integrated density of states for Schrödinger operators with magnetic fields and unbounded random potentials

Details Existence and uniqueness of the integrated density of states for Schrödinger operators with magnetic fields and unbounded random potentials Existence and uniqueness of the integrated density of states for Schrödinger operators with magnetic fields and unbounded random potentials

2000-10-10

arxiv.org/abs/math-ph/0010013v3

Reviews in Mathematical Physics 13 (2001) 1547-1581

Physics

Mathematical Physics

This paper is a revised version of the first part of the first version of math-ph/0010013. For a revised version of the second

Scientific paper

10.1142/S0129055X01001083

The object of the present study is the integrated density of states of a quantum particle in multi-dimensional Euclidean space which is characterized by a Schr\"odinger operator with a constant magnetic field and a random potential which may be unbounded from above and from below. For an ergodic random potential satisfying a simple moment condition, we give a detailed proof that the infinite-volume limits of spatial eigenvalue concentrations of finite-volume operators with different boundary conditions exist almost surely. Since all these limits are shown to coincide with the expectation of the trace of the spatially localized spectral family of the infinite-volume operator, the integrated density of states is almost surely non-random and independent of the chosen boundary condition. Our proof of the independence of the boundary condition builds on and generalizes certain results by S. Doi, A. Iwatsuka and T. Mine [Math. Z. {\bf 237} (2001) 335-371] and S. Nakamura [J. Funct. Anal. {\bf 173} (2001) 136-152].

Affiliated with

Also associated with

No associations

Rating

Existence and uniqueness of the integrated density of states for Schrödinger operators with magnetic fields and unbounded random potentials does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Existence and uniqueness of the integrated density of states for Schrödinger operators with magnetic fields and unbounded random potentials, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Existence and uniqueness of the integrated density of states for Schrödinger operators with magnetic fields and unbounded random potentials will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-722671