Article,

The partition function in the Wigner–Kirkwood expansion

, and .
Journal of Physics A: Mathematical and General, 39 (18): L285 (2006)

Abstract

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.

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