基于分数阶环境热浴的非各态历经判据研究

Studies of nonergodic criterion based on the fractional heat bath model

本文从分数阶谱形式的气固耦合模型出发,理论推导出具有幂律记忆核的广义朗之万方程.研究气体分子在自由场和简谐势场中的动力学演化和长时渐进行为,着重分析三种各态历经判据:Khinchin判据、Lee判据以及内在判据和外在表现的适用性.研究结果表明:Khinchin判据适用于广义朗之万方程描述的所有扩散和输运过程;Lee判据并不适用于布朗运动,只能用来区分不同类型的扩散过程;而内在判据和外在表现不仅能够把非各态历经分为两类,同时可以揭示非各态历经的物理内在根源.

The generalized Langevin equation with a power law memory kernel is derived via the gas/solid-surface model with fractional heat bath. Using Lapalce transformation, the dynamic evolution and long-time asymptotic behaviors of the gas particles occurring either in free or harmonic potentials are then investigated. In particular, the validity of three kinds of ergodic criteria is analyzed in detail, including the Khinchin criterion, Lee criterion, and the intrinsic and external behaviors. It is found that the Khinchin criterion holds for all ranges of diffusion and transport processes described by a generalized Langevin equation. Lee criterion is just applied to distinguish diffusion processes. Meanwhile, the intrinsic criterion and external behaviors can not only divide the nonergodicity into two classes but also reveal the underlying physical origins.