标题： 一些排除过程的精确结果 显示英文标题

标题： Some Exact Results for the Exclusion Process

摘要： 非平衡物理的典型模型是不对称简单排斥过程（ASEP），它作为构建模块用于模拟各种低维传输现象，从细胞内交通到量子点。 我们回顾了通过贝特假设方法在周期环系统上获得的一些最新结果。 我们表明，这种方法允许解析地推导出该模型动力学的许多性质，例如谱间隙和电流的生成函数。 我们还讨论了具有$N$种粒子的广义排斥过程的解，并解释了受排队论启发的几何构造如何揭示矩阵乘积表示技术，该技术已被广泛用于推导 ASEP 的精确结果。 显示英文摘要

摘要： The asymmetric simple exclusion process (ASEP) is a paradigm for non-equilibrium physics that appears as a building block to model various low-dimensional transport phenomena, ranging from intracellular traffic to quantum dots. We review some recent results obtained for the system on a periodic ring by using the Bethe Ansatz. We show that this method allows to derive analytically many properties of the dynamics of the model such as the spectral gap and the generating function of the current. We also discuss the solution of a generalized exclusion process with $N$-species of particles and explain how a geometric construction inspired from queuing theory sheds light on the Matrix Product Representation technique that has been very fruitful to derive exact results for the ASEP.