Bounds on the spectral shift function and the density of states

Details Bounds on the spectral shift function and the density of states Bounds on the spectral shift function and the density of states

2004-12-21

arxiv.org/abs/math-ph/0412078v1

Physics

Mathematical Physics

Latex 2e, 15 pages

Scientific paper

We study spectra of Schr\"odinger operators on $\RR^d$. First we consider a pair of operators which differ by a compactly supported potential, as well as the corresponding semigroups. We prove almost exponential decay of the singular values $\mu_n$ of the difference of the semigroups as $n\to \infty$ and deduce bounds on the spectral shift function of the pair of operators. Thereafter we consider alloy type random Schr\"odinger operators. The single site potential $u$ is assumed to be non-negative and of compact support. The distributions of the random coupling constants are assumed to be H\"older continuous. Based on the estimates for the spectral shift function, we prove a Wegner estimate which implies H\"older continuity of the integrated density of states.

Affiliated with

Also associated with

No associations

Rating

Bounds on the spectral shift function and the density of states 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 Bounds on the spectral shift function and the density of states, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Bounds on the spectral shift function and the density of states will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-543409