Abstract
AbstractWe consider the generalized Langevin equation (GLE) in a harmonic potential with power law decay memory. We study the anomalous diffusion of the particle’s displacement and velocity. By comparison with the free particle situation in which the velocity was previously shown to be either diffusive or subdiffusive, we find that, when trapped in a harmonic potential, the particle’s displacement may either be diffusive or superdiffusive. Under slightly stronger assumptions on the memory kernel, namely, for kernels related to the broad class of completely monotonic functions, we show that both the free particle and the harmonically bounded GLE satisfy the equipartition of energy condition. This generalizes previously known results for the GLE under particular kernel instances such as the generalized Rouse kernel or (exactly) a power law function.
Publisher
Springer Science and Business Media LLC
Subject
Mathematical Physics,Statistical and Nonlinear Physics
Reference52 articles.
1. Argun, A., Moradi, A.-R., Pinçe, E., Bagci, G.B., Imparato, A., Volpe, G.: Non-Boltzmann stationary distributions and nonequilibrium relations in active baths. Phys. Rev. E 94(6), 062150 (2016)
2. Brockwell, P.J., Davis, R.A.: Time Series: Theory and Methods. Springer, Berlin (1991)
3. Chandler, D.: Introduction to Modern Statistical Mechanics. Oxford University Press, Oxford (1987)
4. Cramér, H., Leadbetter, R.: Stationary and related stochastic processes: sample function properties and their applications. Courier Corporation, Chelmsford (1967)
5. Desposito, M.A., Viñales, A.D.: Memory effects in the asymptotic diffusive behavior of a classical oscillator described by a generalized Langevin equation. Phys. Rev. E 77(3), 031123 (2008)
Cited by
4 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献