Generalised Ornstein-Uhlenbeck processes
摘要
We solve a physically significant extension of a classic problem in the theory of diffusion, namely the Ornstein-Uhlenbeck process [G. E. Ornstein and L. S. Uhlenbeck, Phys. Rev. 36, 823, (1930)]. Our generalised Ornstein-Uhlenbeck systems include a force which depends upon the position of the particle, as well as upon time. They exhibit anomalous diffusion at short times, and non-Maxwellian velocity distributions in equilibrium. Two approaches are used. Some statistics are obtained from a closed-form expression for the propagator of the Fokker-Planck equation for the case where the particle is initially at rest. In the general case we use spectral decomposition of a Fokker-Planck equation, employing nonlinear creation and annihilation operators to generate the spectrum which consists of two staggered ladders.
引用
@article{arxiv.cond-mat/0602548,
title = {Generalised Ornstein-Uhlenbeck processes},
author = {V. Bezuglyy and B. Mehlig and M. Wilkinson and K. Nakamura and E. Arvedson},
journal= {arXiv preprint arXiv:cond-mat/0602548},
year = {2009}
}
备注
24 pages, 2 figures