Quantum resonances in chaoti scattering

Kevin K. Lin; Maciej Zworski

doi:10.1016/S0009-2614(02)00212-9

Quantum resonances in chaoti scattering

Kevin K. Lin
, Maciej Zworski

Research output: Contribution to journal › Article › peer-review

27 Scopus citations

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 language	English (US)
Pages (from-to)	201-205
Number of pages	5
Journal	Chemical Physics Letters
Volume	355
Issue number	1-2
DOIs	https://doi.org/10.1016/S0009-2614(02)00212-9
State	Published - Mar 25 2002
Externally published	Yes

ASJC Scopus subject areas

General Physics and Astronomy
Physical and Theoretical Chemistry

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10.1016/S0009-2614(02)00212-9

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title = "Quantum resonances in chaoti scattering",

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.",

author = "Lin, \{Kevin K.\} and Maciej Zworski",

note = "Funding Information: We would like to thank Bill Miller for helpful comments on the first version of this Letter. K.L. was supported by the Fannie and John Hertz Foundation. M.Z. was partly supported by the NSF under grant DMS-9970614. ",

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AU - Lin, Kevin K.

AU - Zworski, Maciej

N1 - Funding Information: We would like to thank Bill Miller for helpful comments on the first version of this Letter. K.L. was supported by the Fannie and John Hertz Foundation. M.Z. was partly supported by the NSF under grant DMS-9970614.

PY - 2002/3/25

Y1 - 2002/3/25

N2 - 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.

AB - 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.

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DO - 10.1016/S0009-2614(02)00212-9

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JO - Chemical Physics Letters

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Quantum resonances in chaoti scattering

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