周期场中非各态历经布朗运动

将自由状态下呈弹道扩散的非各态历经系统置于周期场中，进而将非各态历经布朗运动分为两类.第一类是阻尼核的Laplace变换的低频为零的系统，当温度远大于势垒高度时，系统平均能量的动能部分依赖粒子的初始速度分布；随温度降低，系统的各态历经性得到恢复.然后将第一类系统的稳定速度变量作为一个内部噪声，再去驱动一个自由布朗粒子，则阻尼核的Laplace变换在零频时为无穷大.结果发现，粒子扩散系数随温度的增加而趋于零，显示一种经典局域化特征，系统的渐进分布依赖于初始坐标分布.这是第二类非各态历经性运动，不能通过外加势而恢复. 关键词： 非各态历经 非Markov布朗运动 扩散系数 噪声谱

Nonergodicity of Brownian motion in a periodic potential

Nonergodicity in Brownian dynamics can be divided into two classes by adding a periodic potential in a force-free ballistic diffusive system. Class-I is the system in which the Laplace transform of the damping kernel is equal to zero at low frequency.When the temperature is much higher than the barrier height, the kinetic part of the mean energy depends on the initial distribution of the velocity; with the temperature decreasing, the ergodicity is recovered. Thinking the stable velocity variance of class-I as an internal noise to drive a force-free Brownian particle, the Laplace transform of the damping kernel is infinite at zero frequency. It is found that the diffusion coefficient approaches vanishing with the temperature increasing, which exhibits the characteristic of classical locality. The asymptotic mean-square coordinates of the class-l] depends on its initial coordinates and the ergodicity cannot be ensured through introducing a potential.