Quantum Arnol'd diffusion in a rippled waveguide

We study the quantum Arnol'd diffusion for a particle moving in a quasi-1D waveguide bounded by a periodically rippled surface, in the presence of the time-periodic electric field. It was found that in a deep semiclassical region the diffusion-like motion occurs for a particle in the region corresponding to a stochastic layer surrounding the coupling resonance. The rate of the quantum diffusion turns out to be less than the corresponding classical one, thus indicating the influence of quantum coherent effects. Another result is that even in the case when such a diffusion is possible, it terminates in time due to the mechanism similar to that of the dynamical localization. The quantum Arnol'd diffusion represents a new type of quantum dynamics, and may be experimentally observed in measurements of a conductivity of low-dimensional mesoscopic structures.Comment: 13 pages, 3 figure

Quantum Ergodicity and Localization in Conservative Systems: the Wigner Band Random Matrix Model

First theoretical and numerical results on the global structure of the energy shell, the Green function spectra and the eigenfunctions, both localized and ergodic, in a generic conservative quantum system are presented. In case of quantum localization the eigenfunctions are shown to be typically narrow and solid, with centers randomly scattered within the semicircle energy shell while the Green function spectral density (local spectral density of states) is extended over the whole shell, but sparse.Comment: 4 pages in RevTex and 4 Postscript figures; presented to Phys. Lett.

Evolution of wave packets in quasi-1D and 1D random media: diffusion versus localization

We study numerically the evolution of wavepackets in quasi one-dimensional random systems described by a tight-binding Hamiltonian with long-range random interactions. Results are presented for the scaling properties of the width of packets in three time regimes: ballistic, diffusive and localized. Particular attention is given to the fluctuations of packet widths in both the diffusive and localized regime. Scaling properties of the steady-state distribution are also analyzed and compared with theoretical expression borrowed from one-dimensional Anderson theory. Analogies and differences with the kicked rotator model and the one-dimensional localization are discussed.Comment: 32 pages, LaTex, 11 PostScript figure

Nonlinearity effects in the kicked oscillator

The quantum kicked oscillator is known to display a remarkable richness of dynamical behaviour, from ballistic spreading to dynamical localization. Here we investigate the effects of a Gross Pitaevskii nonlinearity on quantum motion, and provide evidence that the qualitative features depend strongly on the parameters of the system.Comment: 4 pages, 5 figure

Kolmogorov turbulence, Anderson localization and KAM integrability

The conditions for emergence of Kolmogorov turbulence, and related weak wave turbulence, in finite size systems are analyzed by analytical methods and numerical simulations of simple models. The analogy between Kolmogorov energy flow from large to small spacial scales and conductivity in disordered solid state systems is proposed. It is argued that the Anderson localization can stop such an energy flow. The effects of nonlinear wave interactions on such a localization are analyzed. The results obtained for finite size system models show the existence of an effective chaos border between the Kolmogorov-Arnold-Moser (KAM) integrability at weak nonlinearity, when energy does not flow to small scales, and developed chaos regime emerging above this border with the Kolmogorov turbulent energy flow from large to small scales.Comment: 8 pages, 6 figs, EPJB style

Quantum Computing of Quantum Chaos in the Kicked Rotator Model

We investigate a quantum algorithm which simulates efficiently the quantum kicked rotator model, a system which displays rich physical properties, and enables to study problems of quantum chaos, atomic physics and localization of electrons in solids. The effects of errors in gate operations are tested on this algorithm in numerical simulations with up to 20 qubits. In this way various physical quantities are investigated. Some of them, such as second moment of probability distribution and tunneling transitions through invariant curves are shown to be particularly sensitive to errors. However, investigations of the fidelity and Wigner and Husimi distributions show that these physical quantities are robust in presence of imperfections. This implies that the algorithm can simulate the dynamics of quantum chaos in presence of a moderate amount of noise.Comment: research at Quantware MIPS Center http://www.quantware.ups-tlse.fr, revtex 11 pages, 13 figs, 2 figs and discussion adde

Quantum resonant effects in the delta-kicked rotor revisited

We review the theoretical model and experimental realization of the atom optics $\delta-$kicked rotor (AOKR), a paradigm of classical and quantum chaos. We have performed a number of experiments with an all-optical Bose-Einstein condensate (BEC) in a periodic standing wave potential in an AOKR system. We discuss results of the investigation of the phenomena of quantum resonances in the AOKR. An interesting feature of the momentum distribution of the atoms obtained as a result of short pulses of light, is the variance of the momentum distribution or the kinetic energy $/2m$ in units of the recoil energy $E_{rec} = \hbar \omega_{rec}$. The energy of the system is examined as a function of pulse period for a range of kicks that allow the observation of quantum resonances. In particular we study the behavior of these resonances for a large number of kicks. Higher order quantum resonant effects corresponding to the fractional Talbot time of (1/4)$T_{T}$ and (1/5)$T_{T}$ for five and ten kicks have been observed. Moreover, we describe the effect of the initial momentum of the atoms on quantum resonances in the AOKR.Comment: 30 pages, 17 figure

A fractional approach to the Fermi-Pasta-Ulam problem

This paper studies the Fermi-Pasta-Ulam problem having in mind the generalization provided by Fractional Calculus (FC). The study starts by addressing the classical formulation, based on the standard integer order differential calculus and evaluates the time and frequency responses. A first generalization to be investigated consists in the direct replacement of the springs by fractional elements of the dissipative type. It is observed that the responses settle rapidly and no relevant phenomena occur. A second approach consists of replacing the springs by a blend of energy extracting and energy inserting elements of symmetrical fractional order with amplitude modulated by quadratic terms. The numerical results reveal a response close to chaotic behaviour