Large Deviations of a Tracer in the Symmetric Exclusion Process
Large Deviations of a Tracer in the Symmetric Exclusion Process
复制标题
DOI：
10.1103/physrevlett.118.160601
复制
发表时间：
2017-04-17
影响因子：
8.6
通讯作者：
Sasamoto, Tomohiro
中科院分区：
文献类型：
--
作者：
Imamura, Takashi;Mallick, Kirone;Sasamoto, Tomohiro
一维对称不相容过程是最简单的粒子相互作用过程，它是一种晶格气体，由粒子在一条离散线上对称地跳跃，尊重核心不相容。该系统是在无限晶格上制备的，具有阶梯初始轮廓，平均密度在原点的左右两侧分别为rho（+）和rho（-）。当rho(+) = rho（-）时，气体处于平衡状态，并经历平稳波动。当这些密度不相等时，气体就会失去平衡，并将永远保持这种状态。示踪剂或标记粒子最初位于两个区域之间的边界；它的位置X-t是一个随机的时间观测值，它携带着整个系统的非平衡动力学信息。我们推导出了X-t在长时间极限下的累积量生成函数和大偏差函数的精确公式，并推导出了示踪剂位置的全部统计性质。当密度均匀时，示踪剂位置的平衡波动是一个重要的特例。
The one-dimensional symmetric exclusion process, the simplest interacting particle process, is a lattice gas made of particles that hop symmetrically on a discrete line respecting hard-core exclusion. The system is prepared on the infinite lattice with a step initial profile with average densities rho(+) and rho(-) on the right and on the left of the origin. When rho(+) = rho(-), the gas is at equilibrium and undergoes stationary fluctuations. When these densities are unequal, the gas is out of equilibrium and will remain so forever. A tracer, or a tagged particle, is initially located at the boundary between the two domains; its position X-t is a random observable in time that carries information on the nonequilibrium dynamics of the whole system. We derive an exact formula for the cumulant generating function and the large deviation function of X-t in the longtime limit and deduce the full statistical properties of the tracer's position. The equilibrium fluctuations of the tracer's position, when the density is uniform, are obtained as an important special case.