Fractal Weyl Laws for Chaotic Open Systems

W. T. Lu, S. Sridhar, and Maciej Zworski
Phys. Rev. Lett. 91, 154101 – Published 8 October 2003

Abstract

We present a conjecture relating the density of quantum resonances for an open chaotic system to the fractal dimension of the associated classical repeller. Mathematical arguments justifying this conjecture are discussed. Numerical evidence based on computation of resonances of systems of n disks on a plane are presented supporting this conjecture. The result generalizes the Weyl law for the density of states of a closed system to chaotic open systems.

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  • Received 13 August 2002

DOI:https://doi.org/10.1103/PhysRevLett.91.154101

©2003 American Physical Society

Authors & Affiliations

W. T. Lu1, S. Sridhar1, and Maciej Zworski2

  • 1Department of Physics and Electronic Materials Research Institute, Northeastern University, Boston, Massachusetts 02115, USA
  • 2Department of Mathematics, University of California, Berkeley, California 94720, USA

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Issue

Vol. 91, Iss. 15 — 10 October 2003

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