Semiclassical Dynamics in Wigner Phase Space I : Adiabatic Hybrid Wigner Dynamics

TL;DR

This paper introduces Adiabatic Hybrid Wigner Dynamics (AHWD), a new semiclassical method combining DHK and LSC approximations to efficiently simulate quantum dynamics with reduced sign problems.

Contribution

The paper derives the AHWD method, enabling hybrid treatment of system and bath degrees of freedom in Wigner phase space for adiabatic processes, improving accuracy and computational feasibility.

Findings

AHWD captures quantum interference effects accurately.

It significantly reduces the sign problem in complex simulations.

Demonstrates effectiveness on coupled oscillators and vibrational decoherence models.

Abstract

The Wigner phase space formulation of quantum mechanics is a complete framework for quantum dynamic calculations that elegantly highlights connections with classical dynamics. In this series of two articles, building upon previous efforts, we derive the full hierarchy of approximate semiclassical (SC) dynamic methods for adiabatic and non-adiabatic problems in Wigner phase space. In paper I, focusing on adiabatic single surface processes, we derive the well-known Double Herman-Kluk (DHK) approximation for real-time correlation functions in Wigner phase space, and connect it to the Linearized SC (LSC) approximation through a stationary phase approximation. We exploit this relationship to introduce a new hybrid SC method, termed Adiabatic Hybrid Wigner Dynamics (AHWD) that allows for a few important `system' degrees of freedom (dofs) to be treated at the DHK level, while treating the rest of the dofs (the `bath') at the LSC level. AHWD is shown to accurately capture quantum interference effects in models of coupled oscillators, and the decoherence of vibrational probability density of a model I$_2$ Morse oscillator coupled to an Ohmic thermal bath. We show that AHWD significantly mitigates the sign-problem and employs a reduced dimensional prefactor bringing calculations of complex system-bath problems within the reach of SC methods. Paper II focuses on extending this hybrid SC dynamics to nonadiabatic processes.