Fractional dynamics in the L\'evy quantum kicked rotor

We investigate the quantum kicked rotor in resonance subjected to momentum measurements with a L\'evy waiting time distribution. We find that the system has a sub-ballistic behavior. We obtain an analytical expression for the exponent of the power law of the variance as a function of the characteristic parameter of the L\'evy distribution and connect this anomalous diffusion with a fractional dynamics

Quantum-Classical Correspondence for Isolated Systems of Interacting Particles: Localization and Ergodicity in Energy Space

Generic properties of the strength function (local density of states (LDOS)) and chaotic eigenstates are analyzed for isolated systems of interacting particles. Both random matrix models and dynamical systems are considered in the unique approach. Specific attention is paid to the quantum-classical correspondence for the form of the LDOS and eigenstates, and to the localization in the energy shell. New effect of the non-ergodicity of individual eigenstates in a deep semiclassical limit is briefly discussed.Comment: RevTex, 11 pages including 5 Postscript figures, submitted to the Proceedings of the Nobel Simposia "Quantum Chaos Y2K

q-Breathers and the Fermi-Pasta-Ulam Problem

The Fermi-Pasta-Ulam (FPU) paradox consists of the nonequipartition of energy among normal modes of a weakly anharmonic atomic chain model. In the harmonic limit each normal mode corresponds to a periodic orbit in phase space and is characterized by its wave number $q$. We continue normal modes from the harmonic limit into the FPU parameter regime and obtain persistence of these periodic orbits, termed here $q$-Breathers (QB). They are characterized by time periodicity, exponential localization in the $q$-space of normal modes and linear stability up to a size-dependent threshold amplitude. Trajectories computed in the original FPU setting are perturbations around these exact QB solutions. The QB concept is applicable to other nonlinear lattices as well.Comment: 4 pages, 4 figure

Delocalisation transition in quasi-1D models with correlated disorder

We introduce a new approach to analyse the global structure of electronic states in quasi-1D models in terms of the dynamics of a system of parametric oscillators with time-dependent stochastic couplings. We thus extend to quasi-1D models the method previously applied to 1D disordered models. Using this approach, we show that a ``delocalisation transition'' can occur in quasi-1D models with weak disorder with long-range correlations.Comment: 33 pages, no figure

A classical scaling theory of quantum resonances

The quantum resonances occurring with delta-kicked particles are studied with the help of a fictitious classical limit, establishing a direct correspondence between the nearly resonant quantum motion and the classical resonances of a related system. A scaling law which characterizes the structure of the resonant peaks is derived and numerically demonstrated.Comment: 4 pages, 2 Fig