Mathematics – Spectral Theory
Scientific paper
2007-08-03
Oberwolfach Reports, Volume 4, Issue 1, pages 371-416, 2007
Mathematics
Spectral Theory
This is a note for the report on the Oberwolfach Mini-Workshop: Multiscale and Variational Methods in Material Science and Qua
Scientific paper
In various aspects of the spectral analysis of random Schroedinger operators monotonicity with respect to the randomness plays a key role. In particular, both the continuity properties and the low energy behaviour of the integrated density of states (IDS) are much better understood if such a monotonicity is present in the model than if not. In this note we present Lifshitz-type bounds on the IDS for two classes of random potentials. One of them is a slight generalisation of a model for which a Lifshitz bound was derived in a recent joint paper with Werner Kirsch [KV]. The second one is a breather type potential which is a sum of characteristic functions of intervals. Although the second model is very simple, it seems that it cannot be treated by the methods of [KV]. The models and the proofs are motivated by well-established methods developed for so called alloy type potentials.
No associations
LandOfFree
Lifshitz asymptotics for Hamiltonians monotone in the randomness 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 Lifshitz asymptotics for Hamiltonians monotone in the randomness, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Lifshitz asymptotics for Hamiltonians monotone in the randomness will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-602002