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APS » Journals » Phys. Rev. Lett. » Volume 75 » Issue 24
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Phys. Rev. Lett. 75, 4346–4349 (1995)

Semiclassical Trace Formulas of Near-Integrable Systems: Resonances

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Steven Tomsovic1, Maurice Grinberg2,*, and Denis Ullmo3,†
1Department of Physics, Washington State University, Pullman, Washington 99164-2814
2Division de Physique Théorique, Institut de Physique Nucléaire, 91406 Orsay CEDEX, France
3AT&T Bell Laboratories, 1D-265, 600 Mountain Avenue, Murray Hill, New Jersey 07974

Received 16 June 1995; published in the issue dated 11 December 1995

Trace formulas relate the quantum density of states to the properties of the periodic orbits of the underlying classical system. The expressions depend critically on the nature of the classical dynamics. The near-integrable regime is most importantly characterized by the destruction of rational invariant tori being replaced by chains of resonances, yet without globalized chaos being introduced. We give new, generalized expressions appropriate for resonances and apply them to a system that has served as a paradigm for the transition from regular to chaotic dynamics.

© 1995 The American Physical Society

URL:
http://link.aps.org/doi/10.1103/PhysRevLett.75.4346
DOI:
10.1103/PhysRevLett.75.4346
PACS:
03.65.Sq, 03.20.+i, 05.45.+b

*Permanent address: Institute for Nuclear Research and Nuclear Energy, Bulgarian Academy of Sciences, 72 "Tzarigrad Road," 1784 Sofia, Bulgaria.

†Permanent address: Division de Physique Théorique, IPN, 91406 Orsay CEDEX, France.

 
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