Nonequilibrium statistical mechanics, Solvable one-dimensional systems, Large deviations

点击翻译按钮获取中文摘要

Lately a lot of research was devoted to the understanding the effects of fluctuations in low-dimensional stochastic models. Since one is interested in phase transitions and in gapless phases, it is important to have models which are solvable using analytic methods. One class of models of this kind are manycomponent diffusion models which are obtained using Hamiltonians written in terms of generators of the Hecke algebras [1]. Our aim is to consider applications of the Birman-Murakami-Wenzl algebras (BMW) [2]. This is not a simple generalization since, as a simple example shows [3], one obtains in this way also "chemical" reactions not only diffusion. New physics will show up which makes this study fascinating.Large deviations theory [4] is also a subject of major interest since it allows to define quantities like entropy and free energy for nonequilibrium systems. Up to now models with local interactions were studied only. We plan to consider large deviations of the current in the Raise and Peel model [5] which is solvable, with nonlocal interactions and has a space-time symmetry (conformal invariance).