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Название: Spectral Fluctuations of Schrodinger Operators Generated by Critical Points of the Potential
Автор: Camus B.
Starting from the spectrum of Schrodinger operators on R^n, we propose a method to detect critical points of the potential. We argue semi-classically on the basis of a mathematically rigorous version of Gutzwiller’s trace formula which expresses spectral statistics in term of classical orbits. A critical point of the potential with zero momentum is an equilibrium of the ﬂow and generates certain singularities in the spectrum. Via sharp spectral estimates, this ﬂuctuation indicates the presence of a critical point and allows to reconstruct partially the local shape of the potential. Some generalizations of this approach are also proposed