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

本项目致力于复杂粘弹性介质中的异常慢扩散。这种亚扩散的典型特征是布朗粒子位移的长时间反相关，而不是在捕获域中分散的平均停留时间。它可以用幂律的广义朗之万方程来描述，该方程具有衰减记忆摩擦和与波动耗散定理相关的分数阶高斯噪声。这个项目将利用一个互补的和更现实的方法，其中内存核是由一个有限的指数求和近似显示分形缩放。这允许深度非马尔可夫随机动力学的多维马尔可夫嵌入，并有利于利用为马尔可夫系统开发的成熟方法。该项目的重点是：(i)双稳态亚扩散动力学，模拟大分子中由于固有粘弹性或环境粘弹性（例如生物膜中的酶或离子通道）引起的构象转变，以及（ii）空间周期性结构中的粘弹性传输，特别是由时间周期场驱动的热平衡。一些新的异常非平衡现象，如亚扩散摇摆棘轮，将被研究。

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.