### 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) |
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Pages (from-to) | 201-205 |

Number of pages | 5 |

Journal | Chemical Physics Letters |

Volume | 355 |

Issue number | 1-2 |

DOIs | |

State | Published - Mar 25 2002 |

Externally published | Yes |

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### ASJC Scopus subject areas

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

### Cite this

*Chemical Physics Letters*,

*355*(1-2), 201-205. https://doi.org/10.1016/S0009-2614(02)00212-9

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

Research output: Contribution to journal › Article

*Chemical Physics Letters*, vol. 355, no. 1-2, pp. 201-205. https://doi.org/10.1016/S0009-2614(02)00212-9

}

TY - JOUR

T1 - Quantum resonances in chaoti scattering

AU - Lin, Kevin

AU - Zworski, Maciej

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.

UR - http://www.scopus.com/inward/record.url?scp=0037170970&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0037170970&partnerID=8YFLogxK

U2 - 10.1016/S0009-2614(02)00212-9

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

M3 - Article

AN - SCOPUS:0037170970

VL - 355

SP - 201

EP - 205

JO - Chemical Physics Letters

JF - Chemical Physics Letters

SN - 0009-2614

IS - 1-2

ER -