6,551 research outputs found

    Minimal length scales for the existence of local temperature

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    We review a recent approach to determine the minimal spatial length scales on which local temperature exists. After mentioning an experiment where such considerations are of relevance, we first discuss the precise definition of the existence of local temperature and its physical relevance. The approach to calculate the length scales in question considers homogenous chains of particles with nearest neighbor interactions. The entire chain is assumed to be in a thermal equilibrium state and it is analyzed when such an equilibrium state at the same time exists for a local part of it. The result yields estimates for real materials, the liability of which is discussed in the sequel. We finally consider a possibility to detect the existence or non-existence of a local thermal state in experiment.Comment: review, 13 pages, 11 figure

    Local Versus Global Thermal States: Correlations and the Existence of Local Temperatures

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    We consider a quantum system consisting of a regular chain of elementary subsystems with nearest neighbor interactions and assume that the total system is in a canonical state with temperature TT. We analyze under what condition the state factors into a product of canonical density matrices with respect to groups of nn subsystems each, and when these groups have the same temperature TT. While in classical mechanics the validity of this procedure only depends on the size of the groups nn, in quantum mechanics the minimum group size nminn_{min} also depends on the temperature TT ! As examples, we apply our analysis to a harmonic chain and different types of Ising spin chains. We discuss various features that show up due to the characteristics of the models considered. For the harmonic chain, which successfully describes thermal properties of insulating solids, our approach gives a first quantitative estimate of the minimal length scale on which temperature can exist: This length scale is found to be constant for temperatures above the Debye temperature and proportional to T3T^{-3} below.Comment: 12 pages, 5 figures, discussion of results extended, accepted for publication in Phys. Rev.

    Operator entanglement of two-qubit joint unitary operations revisited: Schmidt number approach

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    Operator entanglement of two-qubit joint unitary operations is revisited. Schmidt number is an important attribute of a two-qubit unitary operation, and may have connection with the entanglement measure of the unitary operator. We found the entanglement measure of two-qubit unitary operators is classified by the Schmidt number of the unitary operators. The exact relation between the operator entanglement and the parameters of the unitary operator is clarified too.Comment: To appear in the Brazilian Journal of Physic

    Initial results of multilevel principal components analysis of facial shape

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    Traditionally, active shape models (ASMs) do not make a distinction between groups in the subject population and they rely on methods such as (single-level) principal components analysis (PCA). Multilevel principal components analysis (PCA) allows one to model between-group effects and within-group effects explicitly. Three dimensional (3D) laser scans were taken from 240 subjects (38 Croatian female, 35 Croatian male, 40 English female, 40 English male, 23 Welsh female, 27 Welsh male, 23 Finnish female, and 24 Finnish male) and 21 landmark points were created subsequently for each scan. After Procrustes transformation, eigenvalues from mPCA and from single-level PCA based on these points were examined. mPCA indicated that the first two eigenvalues of largest magnitude related to within-groups components, but that the next largest eigenvalue related to between-groups components. Eigenvalues from single-level PCA always had a larger magnitude than either within-group or between-group eigenvectors at equivalent eigenvalue number. An examination of the first mode of variation indicated possible mixing of between-group and within-group effects in single-level PCA. Component scores for mPCA indicated clustering with country and gender for the between-groups components (as ex-pected), but not for the within-group terms (also as expected). Clustering of component scores for single-level PCA was harder to resolve. In conclusion, mPCA is viable method of forming shape models that offers distinct advantages over single-level PCA when groups occur naturally in the subject population

    Fidelity and Concurrence of conjugated states

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    We prove some new properties of fidelity (transition probability) and concurrence, the latter defined by straightforward extension of Wootters notation. Choose a conjugation and consider the dependence of fidelity or of concurrence on conjugated pairs of density operators. These functions turn out to be concave or convex roofs. Optimal decompositions are constructed. Some applications to two- and tripartite systems illustrate the general theorem.Comment: 10 pages, RevTex, Correction: Enlarged, reorganized version. More explanation

    Weak Chaos and the "Melting Transition" in a Confined Microplasma System

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    We present results demonstrating the occurrence of changes in the collective dynamics of a Hamiltonian system which describes a confined microplasma characterized by long--range Coulomb interactions. In its lower energy regime, we first detect macroscopically, the transition from a "crystalline--like" to a "liquid--like" behavior, which we call the "melting transition". We then proceed to study this transition using a microscopic chaos indicator called the \emph{Smaller Alignment Index} (SALI), which utilizes two deviation vectors in the tangent dynamics of the flow and is nearly constant for ordered (quasi--periodic) orbits, while it decays exponentially to zero for chaotic orbits as exp((λ1λ2)t)\exp(-(\lambda_{1}-\lambda_{2})t), where λ1>λ2>0\lambda_{1}>\lambda_{2}>0 are the two largest Lyapunov exponents. During the "melting phase", SALI exhibits a peculiar, stair--like decay to zero, reminiscent of "sticky" orbits of Hamiltonian systems near the boundaries of resonance islands. This alerts us to the importance of the Δλ=λ1λ2\Delta\lambda=\lambda_{1}-\lambda_{2} variations in that regime and helps us identify the energy range over which "melting" occurs as a multi--stage diffusion process through weakly chaotic layers in the phase space of the microplasma. Additional evidence supporting further the above findings is given by examining the GALIkGALI_{k} indices, which generalize SALI (=GALI2GALI_{2}) to the case of k>2k>2 deviation vectors and depend on the complete spectrum of Lyapunov exponents of the tangent flow about the reference orbit.Comment: 21 pages, 7 figures, submitted at PR

    Complete Next to Leading Order QCD Corrections to the Photon Structure Functions F2γ(x,Q2)F^\gamma_2(x,Q^2) and FLγ(x,Q2)F_L^\gamma(x,Q^2)

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    We present the complete NLO QCD analysis of the photon structure functions F2γ(x,Q2)F_2^\gamma(x,Q^2) and FLγ(x,Q2)F_L^\gamma(x,Q^2) for a real photon target. In particular we study the heavy flavor content of the structure functions which is due to two different production mechanisms, namely collisions of a virtual photon with a real photon, and with a parton. We observe that the charm contributions are noticeable for F2γ(x,Q2)F_2^\gamma(x,Q^2) as well as FLγ(x,Q2)F_L^\gamma(x,Q^2) in the x-region studied.Comment: Latex 34 pages, 24 figures, uuencoded, attached at end, ITP-SB-93-46, FERMILAB-Pub-93/240-T, SMU HEP 93-1

    Inelastic x-ray scattering investigations of lattice dynamics in SmFeAsO1x_{1-x}Fy_y superconductors

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    We report measurements of the phonon density of states as measured with inelastic x-ray scattering in SmFeAsO1x_{1-x}Fy_y powders. An unexpected strong renormalization of phonon branches around 23 meV is observed as fluorine is substituted for oxygen. Phonon dispersion measurements on SmFeAsO1x_{1-x}Fy_y single crystals allow us to identify the 21 meV A1g_{1g} in-phase (Sm,As) and the 26 meV B1g_{1g} (Fe,O) modes to be responsible for this renormalization, and may reveal unusual electron-phonon coupling through the spin channel in iron-based superconductors.Comment: 4 pages, 3 figures, submitted for SNS2010 conference proceeding
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