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.
ASJC Scopus subject areas
- Physics and Astronomy(all)
- Physical and Theoretical Chemistry