Poissonization of Quantum Dynamics and Its Applications

Abstract

Simulating nonadiabatic quantum dynamics in molecular systems remains a significant computational challenge because of the complexity of coupled electronic and nuclear motion. We establish an exact correspondence between quantum dynamics and a Poisson process by interpreting the action of the Hamiltonian as a stochastic event. This Poissonization framework provides a wave function-level representation in which the Dyson expansion is sampled stochastically. For nonadiabatic dynamics, the construction naturally gives rise to a rigorous quantum surface-hopping picture, in which a stochastic wave function evolves on individual potential energy surfaces and undergoes hops governed by Poisson statistics. The method is validated against exact quantum dynamics for the Rabi model, the Tully I model, and the Newns–Anderson model. The framework is inherently parallelizable, scales favorably with system size, and offers a rigorous starting point for developing systematically improvable approximations.