Scaling limits for the generalized Langevin equation
arXiv:2007.16087 · doi:10.1007/s00332-020-09671-4
Abstract
In this paper, we study the diffusive limit of solutions to the generalized Langevin equation (GLE) in a periodic potential. Under the assumption of quasi-Markovianity, we obtain sharp longtime equilibration estimates for the GLE using techniques from the theory of hypocoercivity. We then prove asymptotic results for the effective diffusion coefficient in three limiting regimes: the short memory, the overdamped and the underdamped limits. Finally, we employ a recently developed spectral numerical method in order to calculate the effective diffusion coefficient for a wide range of (effective) friction coefficients, confirming our asymptotic results.
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References in corpus (12)
- Brownian motors: noisy transport far from equilibrium
- Non-Equilibrium Statistical Mechanics of Anharmonic Chains Coupled to Two Heat Baths at Different Temperatures
- Colored-noise thermostats à la carte
- Langevin equation with colored noise for constant-temperature molecular dynamics simulations
- Diffusion on a solid surface: Anomalous is normal
- Non-Equilibrium Statistical Mechanics of Strongly Anharmonic Chains of Oscillators
- Quantitative perturbative study of convergence to equilibrium for collisional kinetic models in the torus
- Entropy Production in Non-Linear, Thermally Driven Hamiltonian Systems
- Exponential Convergence to Non-Equilibrium Stationary States in Classical Statistical Mechanics
- From subdiffusion to superdiffusion of particles on solid surfaces
- Asymptotic analysis for the generalized langevin equation
- From ballistic to diffusive behavior in periodic potentials