# Semiclassical dynamics in the mixed quantum-classical limit

## TL;DR

This paper introduces the AMQC-IVR method, a mixed quantum-classical semiclassical approach that improves computational efficiency and accuracy in calculating quantum correlation functions and reaction rates, especially in weakly coupled systems.

## Contribution

It analytically derives the AMQC-IVR expression, combining filtered classical modes with full semiclassical quantum modes, and demonstrates its effectiveness through numerical examples.

## Key findings

- AMQC-IVR accurately computes quantum correlation functions.
- The method is efficient for systems with weak quantum-classical coupling.
- A separable prefactor approximation reduces computational cost in specific regimes.

## Abstract

The semiclassical Double Herman-Kluk Initial Value Representation is an accurate approach to computing quantum real time correlation functions, but its applications are limited by the need to evaluate an oscillatory integral. In previous work, we have shown that this `sign problem' can be mitigated using the modified Filinov filtration technique to control the extent to which individual modes of the system contribute to the overall phase of the integrand. Here we follow this idea to a logical conclusion: we analytically derive a general expression for the mixed quantum-classical limit of the semiclassical correlation function - AMQC-IVR, where the phase contributions from the `classical' modes of the system are filtered while the `quantum' modes are treated in the full semiclassical limit. We numerically demonstrate the accuracy and efficiency of the AMQC-IVR formulation in calculations of quantum correlation functions and reaction rates using three model systems with varied coupling strengths between the classical and quantum subsystems. We also introduce a separable prefactor approximation that further reduces the computational cost, but is only accurate in the limit of weak coupling between the quantum and classical subsystems.