On a certain semiclassical problem on Wiener spaces
نویسنده
چکیده
We study asymptotic behavior of the spectrum of a Schrödinger type operator LV = L− λV on the Wiener space as λ→∞. Here L denotes the Ornstein-Uhlenbeck operator and V is a nonnegative potential function which has finitely many zero points. For some classes of potential functions, we determine the divergence order of the lowest eigenvalue. Also tunneling effect is studied.
منابع مشابه
Semiclassical limit of the lowest eigenvalue of a Schrödinger operator on a Wiener space Dedicated to Professor Tokuzo Shiga on the occasion of his sixtieth birthday
We study a semiclassical limit of the lowest eigenvalue of a Schrödinger operator on a Wiener space. Key results are semiboundedness theorem of the Schrödinger operator, Laplace-type asymptotic formula and IMS localization formula. We also make a remark on semiclassical problem of a Schrödinger operator on a path space over a Riemannian manifold. MSC: Primary 81Q20, Secondary 60H07, 35J10.
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تاریخ انتشار 2003