Path-integral approach to the Wigner-Kirkwood expansion

Abstract

We study the high-temperature behavior of quantum-mechanical path integrals. Starting from the Feynman-Kac formula, we derive a new functional representation of the Wigner-Kirkwood perturbation expansion for quantum Boltzmann densities. As shown by its applications to different potentials, the presented expansion turns out to be quite efficient in generating analytic form of the higher-order expansion coefficients. To put some flesh on the bare bones we apply the expansion to obtain basic thermodynamic functions of the one-dimensional anharmonic oscillator. Further salient issues, such as generalization to the Bloch density matrix and comparison with the more customary world-line formulation are discussed.

18 pages, RevTeX4, revised version with minor changes, accepted to Phys. Rev. E

References in corpus (2)

• Conduction of Ultracold Fermions Through a Mesoscopic Channel
• Path Integral Monte Carlo Simulation of the Warm-Dense Homogeneous Electron Gas

Cited by in corpus (4)

• Tsallis thermostatics as a statistical physics of random chains
• Local-time representation of path integrals
• Physics and Derivatives: Effective-Potential Path-Integral Approximations of Arrow-Debreu Densities
• Path integral for the quartic oscillator: An accurate analytic formula for the partition function