Semi-classical spectral estimates for Schrodinger operators at a critical level. Case of a degenerate maximum of the potential

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:226

Article

Camus, Brice

关键词: trace formula;    semi-classical analysis;    degenerate oscillatory integrals;    Schrodinger operators;   

DOI  :  10.1016/j.jde.2005.10.003

来源: Elsevier

【 摘 要 】

We study the semi-classical trace formula at a critical energy level for a Schrodinger operator on R-n. We assume here that the potential has a totally degenerate critical point associated to a local maximum. The main result, which establishes the contribution of the associated equilibrium in the trace formula, is valid for all time in a compact subset of R and includes the singularity in t = 0. For these new contributions the asymptotic expansion involves the logarithm of the parameter It. Depending on an explicit arithmetic condition on the dimension and the order of the critical point, this logarithmic contribution can appear in the leading term. (c) 2005 Elsevier Inc. All rights reserved.

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