Lifshitz asymptotics for Hamiltonians monotone in the randomness
| dc.creator | Veselic', Ivan | |
| dc.date | 2007-08-03 | |
| dc.date.accessioned | 2026-07-07T08:22:04Z | |
| dc.date.available | 2026-07-07T08:22:04Z | |
| dc.description | 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. | |
| dc.description | This is a note for the report on the Oberwolfach Mini-Workshop: Multiscale and Variational Methods in Material Science and Quantum Theory of Solids | |
| dc.identifier | https://arxiv.org/abs/0708.0487 | |
| dc.identifier | http://arxiv.org/abs/0708.0487 | |
| dc.identifier | Oberwolfach Reports, Volume 4, Issue 1, pages 371-416, 2007 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/135528 | |
| dc.subject | Spectral Theory | |
| dc.subject | Mathematical Physics | |
| dc.subject | Functional Analysis | |
| dc.subject | 35J10, 82B44 | |
| dc.title | Lifshitz asymptotics for Hamiltonians monotone in the randomness | |
| dc.type | text |