- 99-202 Helffer B., Martinez A.
- Phase Transition in the Semiclassical Regime
(58K, LATeX 2e)
May 31, 99
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Abstract. In continuation with \cite{He1} and an unpublished paper by F.~Daumer
\cite{Da},
we would like to explore the variation of the splitting for a
Schr\"odinger 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 heuristical 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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