%0 Journal Article
%T The Partition Function in the Wigner-Kirkwood expansion
%A S. G. Matinyan
%A B. M¨šller
%J Physics
%D 2006
%I arXiv
%R 10.1088/0305-4470/39/18/L05
%X We study the semiclassical Wigner-Kirkwood (WK) expansion of the partition function $Z(t)$ for arbitrary even homogeneous potentials, starting from the Bloch equation. As is well known, the phase-space kernel of $Z$ satisfies the so-called Uhlenbeck-Beth equation, which depends on the gradients of the potential. We perform a chain of transformations to obtain novel forms of this equation that invite analogies with various physical phenomena and formalisms, such as diffusion processes, the Fokker-Planck equation, and supersymmetric quantum mechanics.
%U http://arxiv.org/abs/quant-ph/0602041v3