Semiclassical Statistical Mechanics

Details Semiclassical Statistical Mechanics Semiclassical Statistical Mechanics

1998-03-18

arxiv.org/abs/quant-ph/9803050v2

AIP Conference Proceedings 419, pp 94-104 (1997)

Physics

Quantum Physics

Invited talk at the La Plata meeting on `Trends in Theoretical Physics', La Plata, April, 1997; 14 pages + 5 ps figures. Some

Scientific paper

10.1063/1.54706

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.

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