2013/09/30 by Petr Jizba, Vaclav Zatloukal
Physics and Astronomy · Mathematics · #cond-mat.stat-mech #math-ph #math.MP #quant-ph
paper · pdf · doi:10.1103/physreve.89.012135
published as Phys.Rev.E89:012135,2014 · 18 pages, RevTeX4, revised version with minor changes, accepted to Phys. Rev. E
arxiv created 2014/01/09 · arxiv updated 2014/01/24
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.