SPECTRAL FLUCTUATION PROPERTIES OF HAMILTONIAN-SYSTEMS -
THE TRANSITION REGION BETWEEN ORDER AND CHAOS
SELIGMAN TH, VERBAARSCHOT JJM, ZIRNBAUER MR JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL
18: (14) 2751-2770 1985
Document type: Article
100 (October 28, 2004)
We study a system with two degrees of freedom that undergoes a transition
from regular motion to chaotic motion. We find that the correlations
of the quantum levels are given by the Poisson ensemble in the integrable
case and by the Wigner-Dyson ensemble in the completely chaotic case.
Inbetween we observe a continous transition between these two limits.
A banded ransom matrix model is constructed to describe this transtion.
Special emphasis is put on so called scale invariant systems.
KeyWords Plus: QUANTUM CHAOS, SPECTRAL CORRELATIONS, RANDOM MATRIX THEORY