Quantum-Classical Limit of Quantum Correlation Functions

TL;DR

This paper derives a quantum-classical limit for equilibrium time correlation functions, enabling simulation of quantum transport properties using hybrid quantum-classical dynamics while maintaining full equilibrium statistical descriptions.

Contribution

It introduces a new quantum-classical correlation function framework that combines quantum equilibrium sampling with classical-like dynamics for quantum systems.

Findings

Provides a formalism for quantum-classical correlation functions.

Enables simulation of quantum transport using surface-hopping dynamics.

Retains full equilibrium statistical description in the hybrid approach.

Abstract

A quantum-classical limit of the canonical equilibrium time correlation function for a quantum system is derived. The quantum-classical limit for the dynamics is obtained for quantum systems comprising a subsystem of light particles in a bath of heavy quantum particles. In this limit the time evolution of operators is determined by a quantum-classical Liouville operator but the full equilibrium canonical statistical description of the initial condition is retained. The quantum-classical correlation function expressions derived here provide a way to simulate the transport properties of quantum systems using quantum-classical surface-hopping dynamics combined with sampling schemes for the quantum equilibrium structure of both the subsystem of interest and its environment.