On statistical mechanics of a single particle in high-dimensional random landscapes

Details On statistical mechanics of a single particle in high-dimensional random landscapes On statistical mechanics of a single particle in high-dimensional random landscapes

2008-01-04

arxiv.org/abs/0801.0732v1

ACTA PHYSICA POLONICA B, vol. 38 (2007), pp. 4055-4066

Physics

Condensed Matter

Disordered Systems and Neural Networks

This is mainly a conference presentation summarizing results of arXiv:0706.3776; arXiv:0711.4006 and arXiv:cond-mat/0610035. T

Scientific paper

We discuss recent results of the replica approach to statistical mechanics of a single classical particle placed in a random N(>>1)-dimensional Gaussian landscape. The particular attention is paid to the case of landscapes with logarithmically growing correlations and to its recent generalisations. Those landscapes give rise to a rich multifractal spatial structure of the associated Boltzmann-Gibbs measure. We also briefly mention related results on counting stationary points of random Gaussian surfaces, as well as ongoing research on statistical mechanics in a random landscape constructed locally by adding many squared Gaussian-distributed terms.

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