TY - JOUR

T1 - Quantum resonances in chaoti scattering

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

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

M3 - Article

AN - SCOPUS:0037170970

SN - 0009-2614

VL - 355

SP - 201

EP - 205

JO - Chemical Physics Letters

JF - Chemical Physics Letters

IS - 1-2

ER -