2,560 research outputs found
Generalized Entropies
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
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
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
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
YMoO (pyrochlore system), SrCrGaO (piled
pairs of Kagom\'e layers) and (HO)Fe(SO)(OH) (jarosite
compound). Despite a very small amount of disorder, all the samples exhibit
many characteristic features of spin glass dynamics below a freezing
temperature , much smaller than their Curie-Weiss temperature .
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 re-initializes ageing and the evolution at the new
temperature is the same as if the system were just quenched from above .
However, as the temperature is raised back to , 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
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
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
The conditional quantum mutual information of a tripartite state
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 and , and that it obeys the duality
relation for a four-party pure state on systems . 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 -R\'enyi generalizations
of the conditional mutual information, some of which we can
prove converge to the conditional mutual information in the limit
. Furthermore, we prove that many of these generalizations
satisfy non-negativity, duality, and monotonicity with respect to local
operations on one of the systems or (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 . We prove that this conjecture is true in some
special cases and when is in a neighborhood of one.Comment: v6: 53 pages, final published versio
Large deviations for polling systems
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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