Irregular Dynamics in a One-Dimensional Bose System

We study many-body quantum dynamics of $\delta$-interacting bosons confined in a one-dimensional ring. Main attention is payed to the transition from the mean-field to Tonks-Girardeau regime using an approach developed in the theory of interacting particles. We analyze, both analytically and numerically, how the Shannon entropy of the wavefunction and the momentum distribution depend on time for a weak and strong interactions. We show that the transition from regular (quasi-periodic) to irregular ("chaotic") dynamics coincides with the onset of the Tonks-Girardeau regime. In the latter regime the momentum distribution of the system reveals a statistical relaxation to a steady state distribution. The transition can be observed experimentally by studying the interference fringes obtained after releasing the trap and letting the boson system expand ballistically.Comment: 4 pages 4 picture

Transition from isolated to overlapping resonances in the open system of interacting fermions

We study the statistical properties of resonance widths and spacings in an open system of interacting fermions at the transition between isolated and overlapping resonances, where a radical change in the width distribution occurs. Our main interest is to reveal how this transition is influenced by the onset of chaos in the internal dynamics as the strength of random two-body interaction between the particles increases. We have found that in the region of overlapped resonances, the fluctuations of the widths (rather than their mean values) are strongly affected by the onset of an internal chaos. The results may be applied to the analysis of neutron cross sections, as well as in the physics of mesoscopic devices with strongly interacting electrons.Comment: 4 pages, 5 figures, corrected version, figures are replace

Internal chaos in an open quantum system: From Ericson to conductance fluctuations

The model of an open Fermi-system is used for studying the interplay of intrinsic chaos and irreversible decay into open continuum channels. Two versions of the model are characterized by one-body chaos coming from disorder or by many-body chaos due to the inter-particle interactions. The continuum coupling is described by the effective non-Hermitian Hamiltonian. Our main interest is in specific correlations of cross sections for various channels in dependence on the coupling strength and degree of internal chaos. The results are generic and refer to common features of various mesoscopic objects including conductance fluctuations and resonance nuclear reactions.Comment: 10 pages, 5 figure

The Fermi-Pasta-Ulam problem: 50 years of progress

A brief review of the Fermi-Pasta-Ulam (FPU) paradox is given, together with its suggested resolutions and its relation to other physical problems. We focus on the ideas and concepts that have become the core of modern nonlinear mechanics, in their historical perspective. Starting from the first numerical results of FPU, both theoretical and numerical findings are discussed in close connection with the problems of ergodicity, integrability, chaos and stability of motion. New directions related to the Bose-Einstein condensation and quantum systems of interacting Bose-particles are also considered.Comment: 48 pages, no figures, corrected and accepted for publicatio

Avoiding Quantum Chaos in Quantum Computation

We study a one-dimensional chain of nuclear $1/2-$spins in an external time-dependent magnetic field. This model is considered as a possible candidate for experimental realization of quantum computation. According to the general theory of interacting particles, one of the most dangerous effects is quantum chaos which can destroy the stability of quantum operations. According to the standard viewpoint, the threshold for the onset of quantum chaos due to an interaction between spins (qubits) strongly decreases with an increase of the number of qubits. Contrary to this opinion, we show that the presence of a magnetic field gradient helps to avoid quantum chaos which turns out to disappear with an increase of the number of qubits. We give analytical estimates which explain this effect, together with numerical data supportingComment: RevTex, 5 pages including 3 eps-figure

Experimental observation of high-order quantum accelerator modes.

Using a freely falling cloud of cold cesium atoms periodically kicked by pulses from a vertical standing wave of laser light, we present the first experimental observation of high-order quantum accelerator modes. This confirms the recent prediction by Fishman, Guarneri, and Rebuzzini [Phys. Rev. Lett.10.1103/PhysRevLett.89.084101 89, 084101 (2002)]. We also show how these accelerator modes can be identified with the stable regions of phase space in a classical-like chaotic system, despite their intrinsically quantum origin

Dynamical fidelity of a solid-state quantum computation

In this paper we analyze the dynamics in a spin-model of quantum computer. Main attention is paid to the dynamical fidelity (associated with dynamical errors) of an algorithm that allows to create an entangled state for remote qubits. We show that in the regime of selective resonant excitations of qubits there is no any danger of quantum chaos. Moreover, in this regime a modified perturbation theory gives an adequate description of the dynamics of the system. Our approach allows to explicitly describe all peculiarities of the evolution of the system under time-dependent pulses corresponding to a quantum protocol. Specifically, we analyze, both analytically and numerically, how the fidelity decreases in dependence on the model parameters.Comment: 9 pages, 6 figures, submitted to PR