Chaotic scattering on graphs

Citation
T. Kottos et U. Smilansky, Chaotic scattering on graphs, PHYS REV L, 85(5), 2000, pp. 968-971
Citations number
16
Categorie Soggetti
Physics
Journal title
PHYSICAL REVIEW LETTERS
ISSN journal
00319007 → ACNP
Volume
85
Issue
5
Year of publication
2000
Pages
968 - 971
Database
ISI
SICI code
0031-9007(20000731)85:5<968:CSOG>2.0.ZU;2-I
Abstract
Quantized, compact graphs are excellent paradigms for quantum chaos in boun ded systems. Connecting them with leads to infinity, we show that they disp lay all the features which characterize quantum chaotic scattering. We deri ve exact expressions for the scattering matrix, and an exact trace formula for the density of resonances. in terms of classical orbits, analogous to t he semiclassical theory of chaotic scattering. A statistical analysis of th e cross sections and resonance parameters compares well with thr prediction s of random matrix theory. Hence, this system is proposed ns a convenient t ool to study the generic behavior of chaotic scattering systems and their s emiclassical description.