Bezuglyy, V.; Mehlig, B.; Wilkinson, Michael; Nakamura, K. and Arvedson, E.
|DOI (Digital Object Identifier) Link:||http://doi.org/10.1063/1.2206878|
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We solve a physically significant extension of a classic problem in the theory of diffusion, namely the Ornstein-Uhlenbeck process [Ornstein and Uhlenbeck, Phys. Rev. 36, 823 (1930)]. Our generalized 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. (c) 2006 American Institute of Physics.
|Item Type:||Journal Article|
|Academic Unit/Department:||Mathematics, Computing and Technology > Mathematics and Statistics
Mathematics, Computing and Technology
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|Date Deposited:||08 May 2009 15:09|
|Last Modified:||15 Jan 2016 11:16|
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