Nonlinear Sciences – Chaotic Dynamics
Scientific paper
2000-06-06
Nonlinear Sciences
Chaotic Dynamics
18 pages, 13 figures, submitted to Phys. Rev. E, companion paper
Scientific paper
10.1103/PhysRevE.63.016208
In a previous Letter [Phys. Rev. Lett. 77, 4158 (1996)], a new correlation measure was introduced that sensitively probes phase space localization properties of eigenstates. It is based on a system's response to varying an external parameter. The measure correlates level velocities with overlap intensities between the eigenstates and some localized state of interest. Random matrix theory predicts the absence of such correlations in chaotic systems whereas in the stadium billiard, a paradigm of chaos, strong correlations were observed. Here, we develop further the theoretical basis of that work, extend the stadium results to the full phase space, study the hbar-dependence, and demonstrate the agreement between this measure and a semiclassical theory based on homoclinic orbits.
Cerruti Nicholas R.
Lakshminarayan Arul
Lefebvre Julie H.
Tomsovic Steven
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