Fokker-Planck equation for coupled anharmonic oscillators: symplectic integration and application to mean-field model of cooperative behavior

Abstract

Kinetics of systems specified by anharmonic, nonconservative and nonlocally coupled model Hamiltonians is reproduced in the Fokker-Planck and imaginary time Schrodinger equation techniques with subsequent symplectic integration. Test solutions focused on dielectric response in ferroelectrics demonstrates potential of this technique even for nonlocal and hardly nonlinear problems of polarization switching, and reassure the H-theorem of global stability [M. Shiino, Phys. Rev. A, Vol 36, pp. 2393-2411 (1987)] in the global coupling and zero driving limit. PACS: 64.60.Cn; 77.80.Dj; 77.80 Fm. Keywords: ferroelectric hysteresis, nonequilibrium thermodynamics, nonadiabatic behaviour.