2,560 research outputs found

    Generalized Entropies

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    We study an entropy measure for quantum systems that generalizes the von Neumann entropy as well as its classical counterpart, the Gibbs or Shannon entropy. The entropy measure is based on hypothesis testing and has an elegant formulation as a semidefinite program, a type of convex optimization. After establishing a few basic properties, we prove upper and lower bounds in terms of the smooth entropies, a family of entropy measures that is used to characterize a wide range of operational quantities. From the formulation as a semidefinite program, we also prove a result on decomposition of hypothesis tests, which leads to a chain rule for the entropy.Comment: 21 page

    Spin Anisotropy and Slow Dynamics in Spin Glasses

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    We report on an extensive study of the influence of spin anisotropy on spin glass aging dynamics. New temperature cycle experiments allow us to compare quantitatively the memory effect in four Heisenberg spin glasses with various degrees of random anisotropy and one Ising spin glass. The sharpness of the memory effect appears to decrease continuously with the spin anisotropy. Besides, the spin glass coherence length is determined by magnetic field change experiments for the first time in the Ising sample. For three representative samples, from Heisenberg to Ising spin glasses, we can consistently account for both sets of experiments (temperature cycle and magnetic field change) using a single expression for the growth of the coherence length with time.Comment: 4 pages and 4 figures - Service de Physique de l'Etat Condense CNRS URA 2464), DSM/DRECAM, CEA Saclay, Franc

    Coupling Lattice Boltzmann and Molecular Dynamics models for dense fluids

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    We propose a hybrid model, coupling Lattice Boltzmann and Molecular Dynamics models, for the simulation of dense fluids. Time and length scales are decoupled by using an iterative Schwarz domain decomposition algorithm. The MD and LB formulations communicate via the exchange of velocities and velocity gradients at the interface. We validate the present LB-MD model in simulations of flows of liquid argon past and through a carbon nanotube. Comparisons with existing hybrid algorithms and with reference MD solutions demonstrate the validity of the present approach.Comment: 14 pages, 5 figure

    The relative influences of disorder and of frustration on the glassy dynamics in magnetic systems

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    The magnetisation relaxations of three different types of geometrically frustrated magnetic systems have been studied with the same experimental procedures as previously used in spin glasses. The materials investigated are Y2_2Mo2_2O7_7 (pyrochlore system), SrCr8.6_{8.6}Ga3.4_{3.4}O19_{19} (piled pairs of Kagom\'e layers) and (H3_3O)Fe3_3(SO4_4)2_2(OH)6_6 (jarosite compound). Despite a very small amount of disorder, all the samples exhibit many characteristic features of spin glass dynamics below a freezing temperature TgT_g, much smaller than their Curie-Weiss temperature θ\theta. The ageing properties of their thermoremanent magnetization can be well accounted for by the same scaling law as in spin glasses, and the values of the scaling exponents are very close. The effects of temperature variations during ageing have been specifically investigated. In the pyrochlore and the bi-Kagom\'e compounds, a decrease of temperature after some waiting period at a certain temperature TpT_p re-initializes ageing and the evolution at the new temperature is the same as if the system were just quenched from above TgT_g. However, as the temperature is raised back to TpT_p, the sample recovers the state it had previously reached at that temperature. These features are known in spin glasses as rejuvenation and memory effects. They are clear signatures of the spin glass dynamics. In the Kagom\'e compound, there is also some rejuvenation and memory, but much larger temperature changes are needed to observe the effects. In that sense, the behaviour of this compound is quantitatively different from that of spin glasses.Comment: latex VersionCorrigee4.tex, 4 files, 3 figures, 5 pages (Proceedings of the International Conference on Highly Frustrated Magnetism (HFM2003), August 26-30, 2003, Institut Laue Langevin (ILL), Grenoble, France

    Decoupling with unitary approximate two-designs

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    Consider a bipartite system, of which one subsystem, A, undergoes a physical evolution separated from the other subsystem, R. One may ask under which conditions this evolution destroys all initial correlations between the subsystems A and R, i.e. decouples the subsystems. A quantitative answer to this question is provided by decoupling theorems, which have been developed recently in the area of quantum information theory. This paper builds on preceding work, which shows that decoupling is achieved if the evolution on A consists of a typical unitary, chosen with respect to the Haar measure, followed by a process that adds sufficient decoherence. Here, we prove a generalized decoupling theorem for the case where the unitary is chosen from an approximate two-design. A main implication of this result is that decoupling is physical, in the sense that it occurs already for short sequences of random two-body interactions, which can be modeled as efficient circuits. Our decoupling result is independent of the dimension of the R system, which shows that approximate 2-designs are appropriate for decoupling even if the dimension of this system is large.Comment: Published versio

    Large Deviations Analysis for Distributed Algorithms in an Ergodic Markovian Environment

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    We provide a large deviations analysis of deadlock phenomena occurring in distributed systems sharing common resources. In our model transition probabilities of resource allocation and deallocation are time and space dependent. The process is driven by an ergodic Markov chain and is reflected on the boundary of the d-dimensional cube. In the large resource limit, we prove Freidlin-Wentzell estimates, we study the asymptotic of the deadlock time and we show that the quasi-potential is a viscosity solution of a Hamilton-Jacobi equation with a Neumann boundary condition. We give a complete analysis of the colliding 2-stacks problem and show an example where the system has a stable attractor which is a limit cycle

    Renyi generalizations of the conditional quantum mutual information

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    The conditional quantum mutual information I(A;BC)I(A;B|C) of a tripartite state ρABC\rho_{ABC} is an information quantity which lies at the center of many problems in quantum information theory. Three of its main properties are that it is non-negative for any tripartite state, that it decreases under local operations applied to systems AA and BB, and that it obeys the duality relation I(A;BC)=I(A;BD)I(A;B|C)=I(A;B|D) for a four-party pure state on systems ABCDABCD. The conditional mutual information also underlies the squashed entanglement, an entanglement measure that satisfies all of the axioms desired for an entanglement measure. As such, it has been an open question to find R\'enyi generalizations of the conditional mutual information, that would allow for a deeper understanding of the original quantity and find applications beyond the traditional memoryless setting of quantum information theory. The present paper addresses this question, by defining different α\alpha-R\'enyi generalizations Iα(A;BC)I_{\alpha}(A;B|C) of the conditional mutual information, some of which we can prove converge to the conditional mutual information in the limit α1\alpha\rightarrow1. Furthermore, we prove that many of these generalizations satisfy non-negativity, duality, and monotonicity with respect to local operations on one of the systems AA or BB (with it being left as an open question to prove that monotoniticity holds with respect to local operations on both systems). The quantities defined here should find applications in quantum information theory and perhaps even in other areas of physics, but we leave this for future work. We also state a conjecture regarding the monotonicity of the R\'enyi conditional mutual informations defined here with respect to the R\'enyi parameter α\alpha. We prove that this conjecture is true in some special cases and when α\alpha is in a neighborhood of one.Comment: v6: 53 pages, final published versio

    Large deviations for polling systems

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    Related INRIA Research report available at : http://hal.inria.fr/docs/00/07/27/62/PDF/RR-3892.pdfInternational audienceWe aim at presenting in short the technical report, which states a sample path large deviation principle for a resealed process n-1 Qnt, where Qt represents the joint number of clients at time t in a single server 1-limited polling system with Markovian routing. The main goal is to identify the rate function. A so-called empirical generator is introduced, which consists of Q t and of two empirical measures associated with S t the position of the server at time t. The analysis relies on a suitable change of measure and on a representation of fluid limits for polling systems. Finally, the rate function is solution of a meaningful convex program
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