Quantum resonances in chaoti scattering

Kevin Lin, Maciej Zworski

Research output: Contribution to journalArticle

25 Citations (Scopus)

Abstract

This Letter summarizes numerical results from [J. Comp. Phys. (to appear)] which show that in quantum systems with chaotic classical dynamics, the number of scattering resonances near an energy E scales like h -(D(KE)+1)/2. Here, K E denotes the subset of the classical energy surface H = E which stays bounded for all time under the flow of H and D(K E) denotes its fractal dimension. Since the number of bound states in a quantum system with n degrees of freedom scales like h -n, this suggests that the quantity (D(K E) + 1)/2 represents the effective number of degrees of freedom in chaotic scattering problems.

Original languageEnglish (US)
Pages (from-to)201-205
Number of pages5
JournalChemical Physics Letters
Volume355
Issue number1-2
DOIs
StatePublished - Mar 25 2002
Externally publishedYes

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degrees of freedom
Scattering
resonance scattering
Fractal dimension
guy wires
scattering
Interfacial energy
set theory
surface energy
fractals
energy

ASJC Scopus subject areas

  • Physical and Theoretical Chemistry
  • Spectroscopy
  • Atomic and Molecular Physics, and Optics

Cite this

Quantum resonances in chaoti scattering. / Lin, Kevin; Zworski, Maciej.

In: Chemical Physics Letters, Vol. 355, No. 1-2, 25.03.2002, p. 201-205.

Research output: Contribution to journalArticle

Lin, Kevin ; Zworski, Maciej. / Quantum resonances in chaoti scattering. In: Chemical Physics Letters. 2002 ; Vol. 355, No. 1-2. pp. 201-205.
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