Low energy properties of the random displacement model

Details Low energy properties of the random displacement model Low energy properties of the random displacement model

2008-08-05

arxiv.org/abs/0808.0670v1

Physics

Mathematical Physics

14 pages, 1 figure

Scientific paper

We study low-energy properties of the random displacement model, a random Schr\"odinger operator describing an electron in a randomly deformed lattice. All periodic displacement configurations which minimize the bottom of the spectrum are characterized. While this configuration is essentially unique for dimension greater than one, there are infinitely many different minimizing configurations in the one-dimensional case. The latter leads to unusual low energy asymptotics for the integrated density of states of the one-dimensional random displacement model. For symmetric Bernoulli-distributed displacements it has a $1/\log^2$-singularity at the bottom of the spectrum. In particular, it is not H\"older-continuous.

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