Semiclassical Statistical Mechanics
Abstract
We use a semiclassical approximation to derive the partition function for an arbitrary potential in one-dimensional Quantum Statistical Mechanics, which we view as an example of finite temperature scalar Field Theory at a point. We rely on Catastrophe Theory to analyze the pattern of extrema of the corresponding path-integral. We exhibit the propagator in the background of the different extrema and use it to compute the fluctuation determinant and to develop a (nonperturbative) semiclassical expansion which allows for the calculation of correlation functions. We discuss the examples of the single and double-well quartic anharmonic oscillators, and the implications of our results for higher dimensions.
Cite
@article{arxiv.quant-ph/9803050,
title = {Semiclassical Statistical Mechanics},
author = {C. A. A. de Carvalho and R. M. Cavalcanti},
journal= {arXiv preprint arXiv:quant-ph/9803050},
year = {2009}
}
Comments
Invited talk at the La Plata meeting on `Trends in Theoretical Physics', La Plata, April, 1997; 14 pages + 5 ps figures. Some cosmetical modifications, and addition of some references which were missing in the previous version