Symplectic integration approach to nonadiabatic polarization response in ferroelectrics: Scalar theory

Kinetics of systems specified by anharmonic, nonconservative and nonlocal model Hamiltonians is reproduced in the Fokker-Planck and imaginary time Schrödinger equation techniques with subsequent symplectic integration, inheriting most advantages from its quantum counterparts and exhibiting dynamic hysteresis, polarization switching, and spatially extended stationary polarization.