438 research outputs found
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 . We continue normal modes from the
harmonic limit into the FPU parameter regime and obtain persistence of these
periodic orbits, termed here -Breathers (QB). They are characterized by time
periodicity, exponential localization in the -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
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