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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    Language: English    Cited References:  28    Times Cited:  100   (October 28, 2004)    

Abstract:
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

Addresses:
MAX PLANCK INST NUCL PHYS, D-6900 HEIDELBERG 1, FED REP GER.
UNIV HEIDELBERG, INST THEORET PHYS, D-6900 HEIDELBERG, FED REP GER.

Publisher:
IOP PUBLISHING LTD, BRISTOL

IDS Number:
ARR77

ISSN:
0305-4470


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