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

近年来，人们对低维随机模型中波动的影响进行了大量的研究。由于人们对相变和无间隙相感兴趣，所以有可以用解析方法求解的模型是很重要的。这类模型中的一类是多分量扩散模型，它是用用Hecke代数生成子表示的哈密顿量得到的。我们的目的是考虑Birman-Murakami-Wenzl代数（BMW）[2]的应用。这不是一个简单的概括，因为，正如一个简单的例子所显示的那样，用这种方法不仅可以得到扩散，还可以得到“化学”反应。新的物理学将会出现，这将使这项研究引人入胜。大偏差理论[4]也是一个重要的兴趣课题，因为它允许定义非平衡系统的熵和自由能等量。到目前为止，只研究了具有局部相互作用的模型。我们计划在Raise和Peel模型[5]中考虑电流的大偏差，这是可解的，具有非局部相互作用并且具有时空对称性（共形不变性）。

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).