标题： 通过受限在格子洛伦兹气体中的维度交叉 显示英文标题

标题： Dimensional crossover via confinement in the lattice Lorentz gas

摘要： 我们考虑一个格点模型，其中追踪粒子在随机分布的静止障碍物存在的情况下移动。 由于障碍物引起的拥挤效应与将格点包裹成圆柱体所施加的准限制相互作用。 我们计算了速度自相关函数，并表明在平衡状态下，随着时时间的推移，系统表现出从二维到一维的维度交叉。 施加一个拉力，并我们用解析方法表征稳态，包括稳态速度和扩散系数。 使用随机模拟来讨论解析结果的有效范围。 我们的计算在障碍物密度的一阶精度下是精确的，适用于任意大的力和限制尺寸。 显示英文摘要

摘要： We consider a lattice model in which a tracer particle moves in the presence of randomly distributed immobile obstacles. The crowding effect due to the obstacles interplays with the quasi-confinement imposed by wrapping the lattice onto a cylinder. We compute the velocity autocorrelation function and show that already in equilibrium the system exhibits a dimensional crossover from two- to one-dimensional as time progresses. A pulling force is switched on and we characterize analytically the stationary state in terms of the stationary velocity and diffusion coefficient. Stochastic simulations are used to discuss the range of validity of the analytic results. Our calculation, exact to first order in the obstacle density, holds for arbitrarily large forces and confinement size.