Variational Calculation of Effective Classical Potential at $T \neq 0$ to Higher Orders

TL;DR

This paper introduces a variational method to accurately compute the partition function of an anharmonic oscillator across all temperatures and coupling strengths, improving upon previous approximations.

Contribution

It develops a new variational approach that systematically enhances the locally harmonic Feynman-Kleinert approximation for path integrals at finite temperatures.

Findings

High-accuracy calculations of the partition function across temperature ranges

Effective classical potential obtained to higher orders

Improved agreement with exact results for anharmonic oscillators

Abstract

Using the new variational approach proposed recently for a systematic improvement of the locally harmonic Feynman-Kleinert approximation to path integrals we calculate the partition function of the anharmonic oscillator for all temperatures and coupling strength with high accuracy.