Semiclassical approximation to the partition function of a particle in D dimensions
Quantum Physics
2009-10-31 v2 Statistical Mechanics
High Energy Physics - Phenomenology
High Energy Physics - Theory
Abstract
We use a path integral formalism to derive the semiclassical series for the partition function of a particle in D dimensions. We analyze in particular the case of attractive central potentials, obtaining explicit expressions for the fluctuation determinant and for the semiclassical two-point function in the special cases of the harmonic and single-well quartic anharmonic oscillators. The specific heat of the latter is compared to precise WKB estimates. We conclude by discussing the possible extension of our results to field theories.
Cite
@article{arxiv.quant-ph/9910055,
title = {Semiclassical approximation to the partition function of a particle in D dimensions},
author = {C. A. A. de Carvalho and R. M. Cavalcanti and E. S. Fraga and S. E. Jorás},
journal= {arXiv preprint arXiv:quant-ph/9910055},
year = {2009}
}
Comments
REVTEX,14 pages, 2 figures, final version to appear in Phys. Rev. E