非整体解析势的形状共振宽度
Width of Shape Resonances for Non Globally Analytic Potentials
摘要：
我们考虑半经典的薛定谔算子与“在一个岛”的潜力，我们假设光滑，除了在无穷远。我们给出了形状共振在井底虚部的渐近展开式。这是Helffer和Sjoestrand在全局解析情形下的一个结果的推广。我们使用一个几乎解析的扩展，以继续WKB的解决方案，以及超出焦散集，并且，对于这种近似的准确性的理由，我们开发了一些精致的microlocal参数在h依赖的小区域。
英文摘要：
We consider the semiclassical Schroedinger operator with a "well in an island" potential, on which we assume smoothness only, except near infinity. We give the asymptotic expansion of the imaginary part of the shape resonance at the bottom of the well. This is a generalization of a result by Helffer and Sjoestrand in the globally analytic case. We use an almost analytic extension in order to continue the WKB solution coming from the well beyond the caustic set, and, for the justification of the accuracy of this approximation, we develop some refined microlocal arguments in h-dependent small regions.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
