Homogenization for Generalized Langevin Equations with Applications to Anomalous Diffusion
arXiv:1902.06496 · doi:10.1007/s00023-020-00889-2
Abstract
We study homogenization for a class of generalized Langevin equations (GLEs) with state-dependent coefficients and exhibiting multiple time scales. In addition to the small mass limit, we focus on homogenization limits, which involve taking to zero the inertial time scale and, possibly, some of the memory time scales and noise correlation time scales. The latter are meaningful limits for a class of GLEs modeling anomalous diffusion. We find that, in general, the limiting stochastic differential equations (SDEs) for the slow degrees of freedom contain non-trivial drift correction terms and are driven by non-Markov noise processes. These results follow from a general homogenization theorem stated and proven here. We illustrate them using stochastic models of particle diffusion.
arXiv comment66 pages
References in corpus (22)
- Stochastic modeling in nanoscale biophysics: Subdiffusion within proteins
- Data-driven parameterization of the generalized Langevin equation
- Origin of hyperdiffusion in generalized Brownian motion
- The Smoluchowski-Kramers limit of stochastic differential equations with arbitrary state-dependent friction
- Multiple-scale stochastic processes: decimation, averaging and beyond
- Markovian embedding of non-Markovian superdiffusion
- Quantum Anti-Zeno Effect
- Asymptotic analysis for the generalized langevin equation
- Generalized Langevin equation and fluctuation-dissipation theorem for particle-bath systems in external oscillating fields
- Superstatistical generalised Langevin equation: non-Gaussian viscoelastic anomalous diffusion
- Ageing underdamped scaled Brownian motion: ensemble and time averaged particle displacements, non-ergodicity, and the failure of the overdamping approximation
- Inevitable Power-law Behavior of Isolated Many-Body Quantum Systems and How It Anticipates Thermalization
- Evidence of hydrodynamic and subdiffusive motion of tracers in a viscoelastic medium
- Markovian embedding of fractional superdiffusion
- The Small-Mass Limit for Langevin Dynamics with Unbounded Coefficients and positive friction
- Small Mass Limit of a Langevin Equation on a Manifold
- From Langevin to generalized Langevin equations for the nonequilibrium Rouse model
- Multiscale systems, homogenization, and rough paths
- The small-mass limit and white-noise limit of an infinite dimensional Generalized Langevin Equation
- Homogenization for a Class of Generalized Langevin Equations with an Application to Thermophoresis
- Generalised Langevin Equation Formulation for Anomalous Diffusion in the Ising Model at the Critical Temperature
- Uncertainty quantification for generalized Langevin dynamics