5,994 research outputs found

    Classical and quantum anomalous diffusion in a system of 2δ\delta-kicked Quantum Rotors

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    We study the dynamics of cold atoms subjected to {\em pairs} of closely time-spaced δ\delta-kicks from standing waves of light. The classical phase space of this system is partitioned into momentum cells separated by trapping regions. In a certain range of parameters it is shown that the classical motion is well described by a process of anomalous diffusion. We investigate in detail the impact of the underlying classical anomalous diffusion on the quantum dynamics with special emphasis on the phenomenon of dynamical localization. Based on the study of the quantum density of probability, its second moment and the return probability we identify a region of weak dynamical localization where the quantum diffusion is still anomalous but the diffusion rate is slower than in the classical case. Moreover we examine how other relevant time scales such as the quantum-classical breaking time or the one related to the beginning of full dynamical localization are modified by the classical anomalous diffusion. Finally we discuss the relevance of our results for the understanding of the role of classical cantori in quantum mechanics.Comment: 9 pages, 3 figure

    The QCD vacuum as a disordered medium: A simplified model for the QCD Dirac operator

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    We model the QCD Dirac operator as a power-law random banded matrix (RBM) with the appropriate chiral symmetry. Our motivation is the form of the Dirac operator in a basis of instantonic zero modes with a corresponding gauge background of instantons. We compare the spectral correlations of this model to those of an instanton liquid model (ILM) and find agreement well beyond the Thouless energy. In the bulk of the spectrum the (dimensionless) Thouless energy of the RBM scales with the square root of system size in agreement with the ILM and chiral perturbation theory. Near the origin the scaling of the (dimensionless) Thouless energy in the RBM remains the same as in the bulk which agrees with chiral perturbation theory but not with the ILM. Finally we discuss how this RBM should be modified in order to describe the spectral correlations of the QCD Dirac operator at the finite temperature chiral restoration transition.Comment: 4 pages, 3 figure

    Quantum quenches in disordered systems: Approach to thermal equilibrium without a typical relaxation time

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    We study spectral properties and the dynamics after a quench of one-dimensional spinless fermions with short-range interactions and long-range random hopping. We show that a sufficiently fast decay of the hopping term promotes localization effects at finite temperature, which prevents thermalization even if the classical motion is chaotic. For slower decays, we find that thermalization does occur. However, within this model, the latter regime falls in an unexpected universality class, namely, observables exhibit a power-law (as opposed to an exponential) approach to their thermal expectation values.Comment: 5 pages, 5 figure

    A one-parameter family of interpolating kernels for Smoothed Particle Hydrodynamics studies

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    A set of interpolating functions of the type f(v)={(sin[v pi/2])/(v pi/2)}^n is analyzed in the context of the smoothed-particle hydrodynamics (SPH) technique. The behaviour of these kernels for several values of the parameter n has been studied either analytically as well as numerically in connection with several tests carried out in two dimensions. The main advantage of this kernel relies in its flexibility because for n=3 it is similar to the standard widely used cubic-spline, whereas for n>3 the interpolating function becomes more centrally condensed, being well suited to track discontinuities such as shock fronts and thermal waves.Comment: 36 pages, 12 figures (low-resolution), published in J.C.