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.