APS » PROLA » Phys. Rev. Lett. » Volume 91 » Issue 15

Phys. Rev. Lett. 91, 154101 (2003) [4 pages]

Fractal Weyl Laws for Chaotic Open Systems
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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

Received 13 August 2002; revised 30 May 2003; published 8 October 2003

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.


©2003 The American Physical Society

URL: http://link.aps.org/abstract/PRL/v91/e154101
DOI: 10.1103/PhysRevLett.91.154101
PACS: 05.45.Mt, 05.45.Ac, 03.65.Sq, 31.15.Gy

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