Non-Linear Correlation Functions and Zero-Point Energy Flow in Mixed Quantum-Classical Semiclassical Dynamics

TL;DR

This paper improves a semiclassical method for simulating quantum-classical systems, accurately capturing zero-point energy flow and correlation functions, and introduces modifications to better match quantum and classical limits.

Contribution

It identifies the origin of inaccuracies in MQC for non-linear correlations and proposes a modification that is exact at time zero and correctly models zero-point energy flow.

Findings

Modified MQC is exact at time zero for all correlation functions.

The approach correctly captures quantum and classical zero-point energy limits.

It can predict and control zero-point energy flow direction.

Abstract

Mixed Quantum Classical (MQC)-IVR is a recently introduced semiclassical framework that allows for selective quantization of the modes of a complex system. In the quantum limit, MQC reproduces the semiclassical Double Herman-Kluk IVR results, accurately capturing nuclear quantum coherences and conserving zero-point energy. However, in the classical limit, while MQC mimics the Husimi-IVR for real-time correlation functions with linear operators, it is significantly less accurate for non-linear correlation functions with errors even at time zero. Here, we identify the origin of this discrepancy in the MQC formulation and propose a modification. We analytically show that the modified MQC approach is exact for all correlation functions at time zero, and in a study of zero-point energy (ZPE) flow, we numerically demonstrate that it correctly obtains the quantum and classical limits as a function of time. Interestingly, while classical-limit MQC simulations show the expected, unphysical ZPE leakage, we find it is possible to predict and even modify the direction of ZPE flow through selective quantization of the system, with the quantum-limit modes accepting energy additions but preserving the minimum quantum mechanically required energy.