Viscoelastic subdiffusion, transport and anomalous rate processes in multistablepotentials: in and out of thermal equilibrium, influence of time-periodic andstochastic fields

本计画致力于研究复杂黏弹性介质中的扩散问题。这种次扩散是典型的长寿命的反相关的布朗粒子位移，而不是分散的平均停留时间在捕获域。它可以用广义朗之万方程来描述，具有幂律衰减的记忆摩擦和由涨落耗散定理联系起来的分数阶高斯噪声。这个项目将利用一个互补的和更现实的方法，其中内存内核是由一个有限的指数表现分形缩放的总和近似。这使得一个多维的马尔可夫嵌入深刻的非马尔可夫随机动态和有益的使用行之有效的方法开发的马尔可夫系统。该项目的重点是：（i）由于固有粘弹性或由于环境的粘弹性（例如生物膜中的酶或离子通道），模拟大分子中构象转变的非连续亚扩散动力学，以及（ii）空间周期性结构中的粘弹性输运，特别是由时间周期性场驱动的热平衡。一些新的异常非平衡现象，如例如subdiffusive摇摆棘轮，将被调查。

This project is devoted to anomalously slow diffusion in complex viscoelastic media. Such subdiffusion is typified by long lived anti-correlations of a Brownian particle displacements rather than by diverging mean residence time in trapping domains. It can be described by Generalized Langevin Equation with a power law decaying memory friction and fractional Gaussian noise related by the fluctuation dissipation theorem. This project will take advantage of a complementary and more realistic approach where the memory kernel is approximated by a finite sum of exponentials exhibiting fractal scaling. This allows for a multi-dimensional Markovian embedding of a profoundly non-Markovian stochastic dynamics and for a beneficial use of well-established methodology developed for Markovian systems. This project is focusing on: (i) bistable subdiffusive dynamics mimicking conformational transitions in macromolecules due to intrinsic viscoelasticity, or due to viscoelasticity of the environment (e.g. enzymes or ionic channels in biological membranes), and (ii) viscoelastic transport in spatially periodic structures, especially driven out of the thermal equilibrium by time-periodic fields. A number of new anomalous nonequilibrium phenomena, such as e.g. subdiffusive rocking ratchets, will be investigated.