37,845 research outputs found

    Quantum Chaos & Quantum Computers

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    The standard generic quantum computer model is studied analytically and numerically and the border for emergence of quantum chaos, induced by imperfections and residual inter-qubit couplings, is determined. This phenomenon appears in an isolated quantum computer without any external decoherence. The onset of quantum chaos leads to quantum computer hardware melting, strong quantum entropy growth and destruction of computer operability. The time scales for development of quantum chaos and ergodicity are determined. In spite the fact that this phenomenon is rather dangerous for quantum computing it is shown that the quantum chaos border for inter-qubit coupling is exponentially larger than the energy level spacing between quantum computer eigenstates and drops only linearly with the number of qubits n. As a result the ideal multi-qubit structure of the computer remains rather robust against imperfections. This opens a broad parameter region for a possible realization of quantum computer. The obtained results are related to the recent studies of quantum chaos in such many-body systems as nuclei, complex atoms and molecules, finite Fermi systems and quantum spin glass shards which are also reviewed in the paper.Comment: Lecture at Nobel symposium on "Quantum chaos", June 2000, Sweden; revtex, 10 pages, 9 figure

    Quantum Chaos at Finite Temperature

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    We use the quantum action to study quantum chaos at finite temperature. We present a numerical study of a classically chaotic 2-D Hamiltonian system - harmonic oscillators with anharmonic coupling. We construct the quantum action non-perturbatively and find temperature dependent quantum corrections in the action parameters. We compare Poincar\'{e} sections of the quantum action at finite temperature with those of the classical action.Comment: Text (LaTeX), Figs. (ps

    Non-Markovian Quantum Dynamics and Classical Chaos

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    We study the influence of a chaotic environment in the evolution of an open quantum system. We show that there is an inverse relation between chaos and non-Markovianity. In particular, we remark on the deep relation of the short time non-Markovian behavior with the revivals of the average fidelity amplitude-a fundamental quantity used to measure sensitivity to perturbations and to identify quantum chaos. The long time behavior is established as a finite size effect which vanishes for large enough environments.Comment: Closest to the published versio

    Quantum chaos in QCD at finite temperature

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    We study complete eigenvalue spectra of the staggered Dirac matrix in quenched QCD on a 63×46^3\times 4 lattice. In particular, we investigate the nearest-neighbor spacing distribution P(s)P(s) for various values of β\beta both in the confinement and deconfinement phase. In both phases except far into the deconfinement region, the data agree with the Wigner surmise of random matrix theory which is indicative of quantum chaos. No signs of a transition to Poisson regularity are found, and the reasons for this result are discussed.Comment: 3 pages, 6 figures (included), poster presented by R. Pullirsch at "Lattice 97", to appear in the proceeding

    Quantum Chaos in the Yang-Mills-Higgs System at Finite Temperature

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    The quantum chaos in the finite-temperature Yang-Mills-Higgs system is studied. The energy spectrum of a spatially homogeneous SU(2) Yang-Mills-Higgs is calculated within thermofield dynamics. Level statistics of the spectra is studied by plotting nearest-level spacing distribution histograms. It is found that finite temperature effects lead to a strengthening of chaotic effects, i.e. spectrum which has Poissonian distribution at zero temperature has Gaussian distribution at finite-temperature.Comment: 6 pages, 5 figures, Revte

    Quantum chaos and QCD at finite chemical potential

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    We investigate the distribution of the spacings of adjacent eigenvalues of the lattice Dirac operator. At zero chemical potential μ\mu, the nearest-neighbor spacing distribution P(s)P(s) follows the Wigner surmise of random matrix theory both in the confinement and in the deconfinement phase. This is indicative of quantum chaos. At nonzero chemical potential, the eigenvalues of the Dirac operator become complex. We discuss how P(s)P(s) can be defined in the complex plane. Numerical results from an SU(3) simulation with staggered fermions are compared with predictions from non-hermitian random matrix theory, and agreement with the Ginibre ensemble is found for μ0.7\mu\approx 0.7.Comment: LATTICE98(hightemp), 3 pages, 10 figure
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