Microcanonical Effective Partition Function for the Anharmonic Oscillator

TL;DR

This paper derives a microcanonical effective partition function for an anharmonic oscillator using Feynman-Hibbs potential, enabling Monte Carlo simulations to approximate quantum thermodynamics.

Contribution

It introduces a new form of the effective Hamiltonian suitable for Monte Carlo methods, bridging classical and quantum thermodynamics for anharmonic systems.

Findings

Numerical evaluation of low-temperature entropy matches quantum results

Derived a Monte Carlo-compatible effective Hamiltonian

Presented a Metropolis function for simulation

Abstract

The microcanonical effective partition function, constructed from a Feynman-Hibbs potential, is derived using generalized ensemble theory. The form of the effective Hamiltonian is amenable to Monte Carlo simulation techniques and the relevant Metropolis function is presented. Using the derived expression for the microcanonical effective partition function, the low-temperature entropy of a proton in an anharmonic potential is numerically evaluated and compared with the exact quantum mechanical canonical result.