The Finite Difference Time Domain Method for Computing Single-Particle Density Matrix

TL;DR

This paper introduces a finite difference time domain method to numerically compute the thermal density matrix of single-particle quantum systems, demonstrating efficiency and accuracy across multiple dimensions.

Contribution

It presents a novel FDTD-based approach for calculating the thermal density matrix, with theoretical foundation, algorithm, and practical examples.

Findings

Efficient numerical computation of density matrices

Accurate determination of thermodynamic properties

Applicability demonstrated in 1D, 2D, and 3D systems

Abstract

A general method for numerical computation of the thermal density matrix of a single-particle quantum system is presented. The Schrodinger equation in imaginary time tau is solved numerically by the finite difference time domain (FDTD) method using a set of initial wave functions at tau=0 . By choosing this initial set appropriately, the set of wave functions generated by the FDTD method can be used to construct the thermal density matrix. The theoretical basis of the method, a numerical algorithm for its implementation, and illustrative examples in one, two and three dimensions are given in this paper. The numerical results show that the procedure is efficient and accurately determines the density matrix and thermodynamic properties of single-particle systems. Extensions of the method to more general cases are briefly indicated.