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.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
