Please use this identifier to cite or link to this item: https://doi.org/10.1103/PhysRevE.84.011104
Title: Fokker-Planck equation with arbitrary dc and ac fields: Continued fraction method
Authors: Lee, C.K. 
Gong, J. 
Issue Date: 6-Jul-2011
Source: Lee, C.K., Gong, J. (2011-07-06). Fokker-Planck equation with arbitrary dc and ac fields: Continued fraction method. Physical Review E - Statistical, Nonlinear, and Soft Matter Physics 84 (1) : -. ScholarBank@NUS Repository. https://doi.org/10.1103/PhysRevE.84.011104
Abstract: The continued fraction method (CFM) is used to solve the Fokker-Planck equation with arbitrary dc and ac fields. With an appropriate choice of basis functions, the Fokker-Planck equation is converted into a set of linear algebraic equations with short-ranged coupling and then CFM is implemented to obtain numerical solutions with high efficiency. Both a proposed perturbative CFM and the numerically exact matrix CFM are used to study the nonlinear response of driven systems, with their results compared to assess the validity regime of the perturbative approach. The proposed perturbative CFM approach needs scalar quantities only and hence is more efficient within its validity regime. Two nonlinear systems of different nature are used as examples: molecular dipole (rotational Brownian motion) and particle in a periodic potential (translational Brownian motion). The associated full dynamics is presented in the compact form of hysteresis loops. It is observed that as the strength of an AC driving field increases, pronounced nonlinear effects are manifested in the deformation of the hysteresis loops. © 2011 American Physical Society.
Source Title: Physical Review E - Statistical, Nonlinear, and Soft Matter Physics
URI: http://scholarbank.nus.edu.sg/handle/10635/52944
ISSN: 15393755
DOI: 10.1103/PhysRevE.84.011104
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