Width of shape resonances for non globally analytic potentials

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Author(s)

Abstract

We consider the semiclassical Schrödinger operator with a <i>well in an island</i> 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 the result by Helffer and Sjöstrand [<b>HeSj1</b>] 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 <i>h</i>-dependent small regions.

Journal

  • Journal of the Mathematical Society of Japan

    Journal of the Mathematical Society of Japan 63(1), 1-78, 2011-01-01

    The Mathematical Society of Japan

References:  25

Codes

  • NII Article ID (NAID)
    10027871208
  • NII NACSIS-CAT ID (NCID)
    AA0070177X
  • Text Lang
    ENG
  • Article Type
    ART
  • ISSN
    00255645
  • NDL Article ID
    10947520
  • NDL Source Classification
    ZM31(科学技術--数学)
  • NDL Call No.
    Z53-A209
  • Data Source
    CJP  NDL  J-STAGE 
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