### 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 |

### ASJC Scopus subject areas

- Physics and Astronomy(all)
- Physical and Theoretical Chemistry

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## Cite this

Lin, K. K., & Zworski, M. (2002). Quantum resonances in chaoti scattering.

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