Fourier Path Integral Monte Carlo Method for the Calculation of the Microcanonical Density of States

Using a Hubbard-Stratonovich transformation coupled with Fourier path integral methods, expressions are derived for the numerical evaluation of the microcanonical density of states for quantum particles obeying Boltzmann statistics. A numerical algorithm is suggested to evaluate the quantum density of states and illustrated on a one-dimensional model system. Typeset using REVTEX 1 Over the past decade there has been considerable progress in the development of path integral [1] approaches to computational quantum statistical mechanics [2,3]. With few exceptions [4] the application of path integral methods have been restricted to simulations in the canonical ensemble. Canonical simulations are amenable to path integral treatments because the canonical density matrix is formally identical to the quantum propagator in imaginary time. The purpose of this note is to show that path integral methods can provide an algorithmic basis for microcanonical simulations as well. We let Ω(E)dE represent the number of energy states between E and E+dE. Throughout this paper we will suppress the dependence of the density of states on the number of particles in the system N and the system volume V for notational convenience. For N indistinguishable particles obeying Boltzmann statistics, we begin with the Fourier path integral expression for the canonical partition function [3] Q(β) = 1 N ! (