Level dynamics: An approach to the study of avoided level crossings and transition to chaos
- Lawrence Berkeley Laboratory, University of California, Berkeley, Berkeley, California 94720 (United States) Department of Modern Physics, Lanzhou University, Lanzhou 730000 (China) Center of Theoretical Physics, Chinese Center of Advanced Science and Technology (World Laboratory), Beijing (China)
- Lawrence Berkeley Laboratory, University of California, Berkeley, Berkeley, California 94720 (United States)
The Dyson-Pechukas level dynamics has been reformulated and made suitable for studying avoided level crossings and transition to chaos. The [ital N]-level dynamics is converted into a many-body problem of one-dimensional Coulomb gas with [ital N]-constituent particles having intrinsic excitations. It is shown that local fluctuation of the level distribution is generated by a large number of avoided level crossings. The role played by avoided level crossings in generating chaoticity in level dynamics is similar to the role played by short-range collisions in causing thermalization in many-body dynamics. Furthermore, the effect of level changing rates in producing avoided level crossings is the same as particle velocities in causing particle-particle collisions. A one-dimensional su(2) Hamiltonian has been constructed as an illustration of the level dynamics, showing how the avoided level crossings cause the transition from a regular distribution to the chaotic Gaussian orthogonal ensemble (GOE) distribution of the levels. The existence of the one-dimensional su(2) Hamiltonian which can show both GOE and Poisson level statistics is remarkable and deserves further investigation.
- DOE Contract Number:
- AC03-76SF00098
- OSTI ID:
- 6610170
- Journal Information:
- Physical Review A; (United States), Vol. 47:5; ISSN 1050-2947
- Country of Publication:
- United States
- Language:
- English
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