Anomalous diffusion and transport processes in the presence of spatial and energy disorder, strong correlation and memory effects, and nonlinear friction

该提案致力于在复杂无序的软玻璃状介质（如复杂聚合物溶液和活细胞的胞质溶胶）的一些通用物理模型中布朗粒子的异常扩散和输运中的非线性、无序和强记忆效应的相互作用，无论是在热平衡处或附近，还是远离热平衡。我们将研究一维和二维分数型亚扩散和输运的空间相关和不相关高斯势的各种模型，这些势由具有代数衰减记忆的广义朗之万方程控制。目的之一是澄清西奈型亚扩散和输运的高斯势与有界能量波动的物理起源。高斯无序和噪声在自然界中的广泛存在使得这个问题在统计物理学中具有重要意义，并且在材料科学、硬物质和软物质物理学以及生物物理学中具有广泛的应用兴趣。此外，还将研究具有记忆的粘弹性摩擦的非线性模型，特别是在非线性多稳态势中的扩散的背景下，也存在与时间相关的驱动场。在这里，我们将发展线性粘弹性布朗动力学的推广，具有对非线性粘弹性的持久记忆。它将在一个非线性麦克斯韦-朗之万模型的粘弹性的基础上，多维马尔可夫嵌入。这个建议的推广考虑到布朗粒子速度的记忆摩擦的依赖性。我们的基础上的物理思想，弹性耦合的粘弹性模式的环境依赖于布朗粒子的速度，干扰这个环境，当它移动的影响下的外部字段。这种非线性摩擦效应的粘弹性亚扩散和运输的作用将得到澄清。此外，我们还将讨论流体动力学记忆效应在这方面的作用，特别是在远离热平衡的运输驱动。特别是，瞬态超扩散制度大大增强驾驶的可能性将得到澄清。

The proposal is devoted to an interplay of nonlinearity, disorder and strong memory effects in anomalous diffusion and transport of Brownian particles in some generic physical models of complex disordered soft glass-like media like complex polymeric solutions and cytosol of living cells, both at or near to the thermal equilibrium, and very far away from it. In particular, we will investigate various models of spatially correlated and uncorrelated Gaussian potentials for one- and two-dimensional fractional type subdiffusion and transport in such potentials governed by generalized Langevin equation with an algebraically decaying memory. One of the purposes is to clarify the physical origin of Sinai type subdiffusion and transport in Gaussian potentials with bounded energy fluctuations. The widespread occurrence of Gaussian disorder and noise in nature makes this problem of fundamental significance in statistical physics, as well as of broad applied interest for material sciences, hard and soft matter physics, and biophysics. Furthermore, nonlinear models of viscoelastic friction with memory will also be studied, especially in the context of diffusion in nonlinear multistable potentials, also in the presence of time-dependent driving fields. Here, we will develop a generalization of linear viscoelastic Brownian dynamics with long-lasting memory towards nonlinear viscoelasticity. It will be done within a nonlinear Maxwell-Langevin model of viscoelasticity based on a multi-dimensional Markovian embedding. This proposed generalization takes into account the dependence of memory friction on the Brownian particle velocity. We base it on the physical idea that the elastic couplings to the viscoelastic modes of environment depend on the velocity of Brownian particle which disturbs this environment when it moves under the influence of an external field. The role of such nonlinear friction effects for viscoelastic subdiffusion and transport will be clarified. Besides, we will also address the role of hydrodynamic memory effects in this context, especially for transport driven far away from thermal equilibrium. In particular, the possibility of a transient superdiffusion regime hugely enhanced by driving will be clarified.