Phase transition in the semiclassical regime. (Q2711622)
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scientific article
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Phase transition in the semiclassical regime. |
scientific article |
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5 July 2001
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Phase transition in the semiclassical regime. (English)
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The authors explore the variation of the splitting for a Schrödinger operator coming from field theory when the potential changes as a function of the temperature from a one-well situation to a double well situation. We are for the moment only able to treat the fixed dimension case. But, because the most interesting thing would be to analyze the dependence on the dimension (in the perspective of applications to statistical mechanics) we have tried to follow some of the steps in the proof with respect to the dimension. All this analysis was strongly motivated by a course by M. Kac where some heuristic discussion based on some Born-Oppenheimer analysis is presented. So our work can be considered as a first attempt for justifying this discussion.
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