2005/02/27 by Brice Camus
Computer Science · Mathematics · Physics and Astronomy · #Advanced Mathematical Modeling in Engineering #Quantum chaos and dynamical systems #Spectral Theory in Mathematical Physics #math.AP #math.SP #physics.class-ph
paper · pdf · doi:10.1016/j.jde.2005.10.003
published as Journal of Differential Equations. Volume 226, Issue 1 , 1 July 2006, Pages 295-322 · 27 pages, perhaps to be revised
arxiv created 2005/02/27 · openalex publication_date 2005/11/15 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study the semi-classical trace formula at a critical energy level for a Schrödinger operator on ℝn. 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 h. 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.