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 | |
| 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