Regularity and chaos in interacting two-body systems.

We study classical and quantum chaos for two interacting particles on the plane. This is the simplest nontrivial case which sheds light on chaos in interacting many-body systems. The system consists of a confining one-body potential, assumed to be a deformed harmonic oscillator, and a two-body interaction of Coulomb type. In general, the dynamics is mixed with regular and chaotic trajectories. The relative roles of the one-body field and the two-body interaction are investigated. Chaos sets in as the strength of the two-body interaction increases. However, the degree of chaoticity strongly depends on the shape of the one-body potential and, for some shapes of the harmonic oscillator, the dynamics remains regular for all values of the two-body interaction. Scaling properties are found for the classical as well as for the quantum mechanical problem.

Phase transitions towards frequency entrainment in large oscillator lattices.

We simulate two-dimensional lattices of pulse-coupled oscillators with random natural frequencies, resembling pacemaker cells in the heart. As coupling increases, this system seems to undergo two phase transitions in the thermodynamic limit. First, the largest cluster of frequency entrained oscillators becomes macroscopic. Second, all oscillators frequency entrain, except possibly some isolated ones. Between the two transitions, the system has features indicating self-organized criticality. To our knowledge, the first transition and the intermediate phase have never been observed before. It remains to be seen if they are generic for large lattices of limit cycle oscillators.

Exact fidelity and full fidelity statistics in regular and chaotic surroundings.

For a prepared state exact expressions for the time-dependent mean fidelity as well as for the mean inverse participation ratio are obtained analytically. The prepared state is taken as an eigenstate of the unperturbed system, and the studied fidelity is identical to the survival probability. The full distribution functions of fidelity in the long-time limit and of inverse participation ratio are studied numerically and analytically. Surprising features such as fidelity revival and nonergodicity are observed. The roles of the coupling coefficients and of complexity of background are studied as well.