The Partition Function in the Wigner-Kirkwood expansion
Quantum Physics
2009-11-13 v3 High Energy Physics - Theory
Abstract
We study the semiclassical Wigner-Kirkwood (WK) expansion of the partition function for arbitrary even homogeneous potentials, starting from the Bloch equation. As is well known, the phase-space kernel of 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.
Cite
@article{arxiv.quant-ph/0602041,
title = {The Partition Function in the Wigner-Kirkwood expansion},
author = {S. G. Matinyan and B. Müller},
journal= {arXiv preprint arXiv:quant-ph/0602041},
year = {2009}
}