Fidelity Decay as an Efficient Indicator of Quantum Chaos

Recent work has connected the type of fidelity decay in perturbed quantum models to the presence of chaos in the associated classical models. We demonstrate that a system's rate of fidelity decay under repeated perturbations may be measured efficiently on a quantum information processor, and analyze the conditions under which this indicator is a reliable probe of quantum chaos and related statistical properties of the unperturbed system. The type and rate of the decay are not dependent on the eigenvalue statistics of the unperturbed system, but depend on the system's eigenvector statistics in the eigenbasis of the perturbation operator. For random eigenvector statistics the decay is exponential with a rate fixed precisely by the variance of the perturbation's energy spectrum. Hence, even classically regular models can exhibit an exponential fidelity decay under generic quantum perturbations. These results clarify which perturbations can distinguish classically regular and chaotic quantum systems.Comment: 4 pages, 3 figures, LaTeX; published version (revised introduction and discussion

Application of serious games to sport, health and exercise

Use of interactive entertainment has been exponentially expanded since the last decade. Throughout this 10+ year evolution there has been a concern about turning entertainment properties into serious applications, a.k.a "Serious Games". In this article we present two set of Serious Game applications, an Environment Visualising game which focuses solely on applying serious games to elite Olympic sport and another set of serious games that incorporate an in house developed proprietary input system that can detect most of the human movements which focuses on applying serious games to health and exercise

Semiclassical spectral correlator in quasi one-dimensional systems

We investigate the spectral statistics of chaotic quasi one dimensional systems such as long wires. To do so we represent the spectral correlation function $R(\epsilon)$ through derivatives of a generating function and semiclassically approximate the latter in terms of periodic orbits. In contrast to previous work we obtain both non-oscillatory and oscillatory contributions to the correlation function. Both types of contributions are evaluated to leading order in $1/\epsilon$ for systems with and without time-reversal invariance. Our results agree with expressions from the theory of disordered systems.Comment: 10 pages, no figure

Universal spectral statistics in Wigner-Dyson, chiral and Andreev star graphs II: semiclassical approach

A semiclassical approach to the universal ergodic spectral statistics in quantum star graphs is presented for all known ten symmetry classes of quantum systems. The approach is based on periodic orbit theory, the exact semiclassical trace formula for star graphs and on diagrammatic techniques. The appropriate spectral form factors are calculated upto one order beyond the diagonal and self-dual approximations. The results are in accordance with the corresponding random-matrix theories which supports a properly generalized Bohigas-Giannoni-Schmit conjecture.Comment: 15 Page

Semiclassical Foundation of Universality in Quantum Chaos

We sketch the semiclassical core of a proof of the so-called Bohigas-Giannoni-Schmit conjecture: A dynamical system with full classical chaos has a quantum energy spectrum with universal fluctuations on the scale of the mean level spacing. We show how in the semiclassical limit all system specific properties fade away, leaving only ergodicity, hyperbolicity, and combinatorics as agents determining the contributions of pairs of classical periodic orbits to the quantum spectral form factor. The small-time form factor is thus reproduced semiclassically. Bridges between classical orbits and (the non-linear sigma model of) quantum field theory are built by revealing the contributing orbit pairs as topologically equivalent to Feynman diagrams.Comment: 4 pages, 2 figures; final version published in PRL, minor change

Coarse-Grained Picture for Controlling Complex Quantum Systems

We propose a coarse-grained picture to control ``complex'' quantum dynamics, i.e., multi-level-multi-level transition with a random interaction. Assuming that optimally controlled dynamics can be described as a Rabi-like oscillation between an initial and final state, we derive an analytic optimal field as a solution to optimal control theory. For random matrix systems, we numerically confirm that the analytic optimal field steers an initial state to a target state which both contains many eigenstates.Comment: jpsj2.cls, 2 pages, 3 figure files; appear in J. Phys. Soc. Jpn. Vol.73, No.11 (Nov. 15, 2004

Spectral fluctuations and 1/f noise in the order-chaos transition regime

Level fluctuations in quantum system have been used to characterize quantum chaos using random matrix models. Recently time series methods were used to relate level fluctuations to the classical dynamics in the regular and chaotic limit. In this we show that the spectrum of the system undergoing order to chaos transition displays a characteristic $f^{-\gamma}$ noise and $\gamma$ is correlated with the classical chaos in the system. We demonstrate this using a smooth potential and a time-dependent system modeled by Gaussian and circular ensembles respectively of random matrix theory. We show the effect of short periodic orbits on these fluctuation measures.Comment: 4 pages, 5 figures. Modified version. To appear in Phys. Rev. Let

Semiclassical Theory for Parametric Correlation of Energy Levels

Parametric energy-level correlation describes the response of the energy-level statistics to an external parameter such as the magnetic field. Using semiclassical periodic-orbit theory for a chaotic system, we evaluate the parametric energy-level correlation depending on the magnetic field difference. The small-time expansion of the spectral form factor $K(\tau)$ is shown to be in agreement with the prediction of parameter dependent random-matrix theory to all orders in $\tau$.Comment: 25 pages, no figur

Ballistic Electron Quantum Transport in Presence of a Disordered Background

Effect of a complicated many-body environment is analyzed on the electron random scattering by a 2D mesoscopic open ballistic structure. A new mechanism of decoherence is proposed. The temperature of the environment is supposed to be zero whereas the energy of the incoming particle $E_{in}$ can be close to or somewhat above the Fermi surface in the environment. The single-particle doorway resonance states excited in the structure via external channels are damped not only because of escape through such channels but also due to the ulterior population of the long-lived environmental states. Transmission of an electron with a given incoming $E_{in}$ through the structure turns out to be an incoherent sum of the flow formed by the interfering damped doorway resonances and the retarded flow of the particles re-emitted into the structure by the environment. Though the number of the particles is conserved in each individual event of transmission, there exists a probability that some part of the electron's energy can be absorbed due to environmental many-body effects. In such a case the electron can disappear from the resonance energy interval and elude observation at the fixed transmission energy $E_{in}$ thus resulting in seeming loss of particles, violation of the time reversal symmetry and, as a consequence, suppression of the weak localization. The both decoherence and absorption phenomena are treated within the framework of a unit microscopic model based on the general theory of the resonance scattering. All the effects discussed are controlled by the only parameter: the spreading width of the doorway resonances, that uniquely determines the decoherence rateComment: 7 pages, 1 figure. The published version. A figure has been added; the list of references has been improved. Some explanatory remarks have been include

Homoclinic Signatures of Dynamical Localization

It is demonstrated that the oscillations in the width of the momentum distribution of atoms moving in a phase-modulated standing light field, as a function of the modulation amplitude, are correlated with the variation of the chaotic layer width in energy of an underlying effective pendulum. The maximum effect of dynamical localization and the nearly perfect delocalization are associated with the maxima and minima, respectively, of the chaotic layer width. It is also demonstrated that kinetic energy is conserved as an almost adiabatic invariant at the minima of the chaotic layer width, and that the system is accurately described by delta-kicked rotors at the zeros of the Bessel functions J_0 and J_1. Numerical calculations of kinetic energy and Lyapunov exponents confirm all the theoretical predictions.Comment: 7 pages, 4 figures, enlarged versio