Tunneling catastrophes of the partition function

Details Tunneling catastrophes of the partition function Tunneling catastrophes of the partition function

1998-03-18

arxiv.org/abs/quant-ph/9803049v1

Braz.J.Phys. 27 (1997) 373-378

Physics

Quantum Physics

5 figures, revtex file

Scientific paper

We use path-integrals to derive a general expression for the semiclassical approximation to the partition function of a one-dimensional quantum-mechanical system. Our expression depends solely on ordinary integrals which involve the potential. For high temperatures, the semiclassical expression is dominated by single closed paths. As we lower the temperature, new closed paths may appear, including tunneling paths. The transition from single to multiple-path regime corresponds to well-defined catastrophes. Tunneling sets in whenever they occur. Our formula fully accounts for this feature.

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