Fractal Weyl law for open quantum chaotic maps

Pages 179-251 from Volume 179 (2014), Issue 1 by Stéphane Nonnenmacher, Johannes Sjöstrand, Maciej Zworski

Abstract

We study a semiclassical quantization of Poincaré maps arising in scattering problems with fractal hyperbolic trapped sets. The main application is the proof of a fractal Weyl upper bound for the number of resonances/scattering poles in small domains near the real axis. This result includes the case of several convex (hard) obstacles satisfying a no-eclipse condition.

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      }
  • [EZB] M. Zworski, Semiclassical Analysis, Providence, RI: Amer. Math. Soc., 2012, vol. 138.
    @book {EZB, MRKEY = {2952218},
      AUTHOR = {Zworski, Maciej},
      TITLE = {Semiclassical Analysis},
      SERIES = {Grad. Studies in Math.},
      VOLUME = {138},
      PUBLISHER = {Amer. Math. Soc.},
      ADDRESS = {Providence, RI},
      YEAR = {2012},
      PAGES = {xii+431},
      ISBN = {978-0-8218-8320-4},
      MRCLASS = {58J40 (35P05 35S05 81Q20)},
      MRNUMBER = {2952218},
      MRREVIEWER = {David Borthwick},
      ZBLNUMBER = {1252.58001},
      }

Keywords
, , ,
DOI
https://doi.org/10.4007/annals.2014.179.1.3
MR
3126568
zbMATH
06260587
Milestones
Received: 11 June 2011
Accepted: 6 November 2012
Published online: 1 January 2014

Authors

Stéphane Nonnenmacher

Institut de Physique Théorique, CEA/DSM/PhT, Unité de recherche associée au CNRS, CEA-Saclay, Gif-sur-Yvette, France

Johannes Sjöstrand

Institut de Mathématiques de Bourgogne, Université de Bourgogne, UFR Science et Techniques, Dijon Cedex, France

Maciej Zworski

University of California at Berkeley, Berkeley, CA