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 |
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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 journal › Article
}
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 -