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

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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.