Symplectic integration approach for metastable systems

TL;DR

This paper introduces a symplectic integration method for modeling metastable systems, capturing complex behaviors like ergodicity breaking and stability, with applications demonstrated through anharmonic Hamiltonian examples.

Contribution

It presents a novel symplectic integration approach for nonadiabatic metastable systems modeled by Fokker-Planck and Schrödinger equations, ensuring stability and accurate response simulation.

Findings

Successfully reproduces ergodicity breaking.

Confirms the H-theorem of global stability.

Models spatially extended responses under external fields.

Abstract

Nonadiabatic behavior of metastable systems modeled by anharmonic Hamiltonians is reproduced by the Fokker-Planck and imaginary time Schrodinger equation scheme with subsequent symplectic integration. Example solutions capture ergodicity breaking, reassure the H-theorem of global stability [M. Shiino, Phys. Rev. A, Vol 36, pp. 2393-2411 (1987)], and reproduce spatially extended response under alternate source fields.