Nonlinear Sciences – Chaotic Dynamics
Scientific paper
2002-10-15
Nonlinear Sciences
Chaotic Dynamics
16 pages, 4 figures, accepted in J. Phys. A, special edition on Random Matrix Theory
Scientific paper
10.1088/0305-4470/36/12/334
In quantum/wave systems with chaotic classical analogs, wavefunctions evolve in highly complex, yet deterministic ways. A slight perturbation of the system, though, will cause the evolution to diverge from its original behavior increasingly with time. This divergence can be measured by the fidelity, which is defined as the squared overlap of the two time evolved states. For chaotic systems, two main decay regimes of either Gaussian or exponential behavior have been identified depending on the strength of the perturbation. For perturbation strengths intermediate between the two regimes, the fidelity displays both forms of decay. By applying a complementary combination of random matrix and semiclassical theory, a uniform approximation can be derived that covers the full range of perturbation strengths. The time dependence is entirely fixed by the density of states and the so-called transition parameter, which can be related to the phase space volume of the system and the classical action diffusion constant, respectively. The accuracy of the approximations are illustrated with the standard map.
Cerruti Nicholas R.
Tomsovic Steven
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