Classical Representation of a Quantum System at Equilibrium

TL;DR

This paper develops a method to represent quantum systems at equilibrium using classical models by matching thermodynamic and structural properties, enabling the use of classical simulation techniques for quantum problems.

Contribution

It introduces a systematic way to derive classical parameters that reproduce quantum thermodynamics and structure, facilitating classical methods for quantum systems.

Findings

Classical parameters are determined to match quantum grand potential.

The method preserves ideal gas and RPA limits.

Practical inversion uses hypernetted chain approximation.

Abstract

A quantum system at equilibrium is represented by a corresponding classical system, chosen to reproduce the thermodynamic and structural properties. The objective is to develop a means for exploiting strong coupling classical methods (e.g., MD, integral equations, DFT) to describe quantum systems. The classical system has an effective temperature, local chemical potential, and pair interaction that are defined by requiring equivalence of the grand potential and its functional derivatives with respect to the external and pair potentials for the classical and quantum systems. Practical inversion of this mapping for the classical properties is effected via the hypernetted chain approximation, leading to representations as functionals of the quantum pair correlation function. As an illustration, the parameters of the classical system are determined approximately such that ideal gas and weak coupling RPA limits are preserved.