Mapping Approach for Quantum-Classical Time Correlation Functions

TL;DR

This paper introduces a quantum-classical mapping approach to compute quantum time correlation functions, enabling simulation of quantum transport properties in large systems without surface-hopping.

Contribution

It develops a novel mapping basis method that combines quantum equilibrium with classical-like dynamics for efficient simulation of quantum correlation functions.

Findings

Derives quantum-classical correlation function expressions suitable for simulation.

Provides a phase space formulation avoiding surface-hopping.

Lays groundwork for new algorithms to compute quantum transport in many-body systems.

Abstract

The calculation of quantum canonical time correlation functions is considered in this paper. Transport properties, such as diffusion and reaction rate coefficients, can be determined from time integrals of these correlation functions. Approximate, quantum-classical expressions for correlation functions, which are amenable to simulation, are derived. These expressions incorporate the full quantum equilibrium structure of the system but approximate the dynamics by quantum-classical evolution where a quantum subsystem is coupled to a classical environment. The main feature of the formulation is the use of a mapping basis where the subsystem quantum states are represented by fictitious harmonic oscillator states. This leads to a full phase space representation of the dynamics that can be simulated without appeal to surface-hopping methods. The results in this paper form the basis for new simulation algorithms for the computation of quantum transport properties of large many-body systems.