40,567 research outputs found

    Holographic Equilibration under External Dynamical Electric Field

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    The holographic equilibration of a far-from-equilibrium strongly coupled gauge theory is investigated. The dynamics of a probe D7-brane in an AdS-Vaidya background is studied in the presence of an external time-dependent electric field. Defining the equilibration times teqct_{eq}^c and teqjt_{eq}^j, at which condensation and current relax to their final equilibrated values, receptively, the smallness of transition time kMk_M or kEk_E is enough to observe a universal behaviour for re-scaled equilibration times kMkE(teqc)2k_M k_E (t_{eq}^c)^{-2} and kMkE(teqj)2k_M k_E (t_{eq}^j)^{-2}. Moreover, regardless of the values for kMk_M and kEk_E, teqc/teqjt_{eq}^c/t_{eq}^j also behaves universally for large enough value of the ratio of the final electric field to final temperature. Then a simple discussion of the static case reveals that teqcteqjt_{eq}^c \leq t_{eq}^j. For an out-of-equilibrium process, our numerical results show that, apart from the cases for which kEk_E is small, the static time ordering persists.Comment: 6 pages, 8 figure

    A Classical String in Lifshitz-Vaidya Geometry

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    We study the time evolution of the expectation value of a rectangular Wilson loop in strongly anisotropic time-dependent plasma using gauge-gravity duality. The corresponding gravity theory is given by describing time evolution of a classical string in the Lifshitz-Vaidya background. We show that the expectation value of the Wilson loop oscillates about the value of the static potential with the same parameters after the energy injection is over. We discuss how the amplitude and frequency of the oscillation depend on the parameters of the theory. In particular, by raising the anisotropy parameter, we observe that the amplitude and frequency of the oscillation increase.Comment: 19 pages, 5 figure

    Enlarged Controllability of Riemann-Liouville Fractional Differential Equations

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    We investigate exact enlarged controllability for time fractional diffusion systems of Riemann-Liouville type. The Hilbert uniqueness method is used to prove exact enlarged controllability for both cases of zone and pointwise actuators. A penalization method is given and the minimum energy control is characterized.Comment: This is a preprint of a paper whose final and definite form is with 'Journal of Computational and Nonlinear Dynamics', ISSN 1555-1415, eISSN 1555-1423, CODEN JCNDDM, available at [http://computationalnonlinear.asmedigitalcollection.asme.org]. Submitted 10-Aug-2017; Revised 28-Sept-2017 and 24-Oct-2017; Accepted 05-Nov-201

    Computing Covers Using Prefix Tables

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    An \emph{indeterminate string} x=x[1..n]x = x[1..n] on an alphabet Σ\Sigma is a sequence of nonempty subsets of Σ\Sigma; xx is said to be \emph{regular} if every subset is of size one. A proper substring uu of regular xx is said to be a \emph{cover} of xx iff for every i1..ni \in 1..n, an occurrence of uu in xx includes x[i]x[i]. The \emph{cover array} γ=γ[1..n]\gamma = \gamma[1..n] of xx is an integer array such that γ[i]\gamma[i] is the longest cover of x[1..i]x[1..i]. Fifteen years ago a complex, though nevertheless linear-time, algorithm was proposed to compute the cover array of regular xx based on prior computation of the border array of xx. In this paper we first describe a linear-time algorithm to compute the cover array of regular string xx based on the prefix table of xx. We then extend this result to indeterminate strings.Comment: 14 pages, 1 figur

    Inferring an Indeterminate String from a Prefix Graph

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    An \itbf{indeterminate string} (or, more simply, just a \itbf{string}) \s{x} = \s{x}[1..n] on an alphabet Σ\Sigma is a sequence of nonempty subsets of Σ\Sigma. We say that \s{x}[i_1] and \s{x}[i_2] \itbf{match} (written \s{x}[i_1] \match \s{x}[i_2]) if and only if \s{x}[i_1] \cap \s{x}[i_2] \ne \emptyset. A \itbf{feasible array} is an array \s{y} = \s{y}[1..n] of integers such that \s{y}[1] = n and for every i2..ni \in 2..n, \s{y}[i] \in 0..n\- i\+ 1. A \itbf{prefix table} of a string \s{x} is an array \s{\pi} = \s{\pi}[1..n] of integers such that, for every i1..ni \in 1..n, \s{\pi}[i] = j if and only if \s{x}[i..i\+ j\- 1] is the longest substring at position ii of \s{x} that matches a prefix of \s{x}. It is known from \cite{CRSW13} that every feasible array is a prefix table of some indetermintate string. A \itbf{prefix graph} \mathcal{P} = \mathcal{P}_{\s{y}} is a labelled simple graph whose structure is determined by a feasible array \s{y}. In this paper we show, given a feasible array \s{y}, how to use \mathcal{P}_{\s{y}} to construct a lexicographically least indeterminate string on a minimum alphabet whose prefix table \s{\pi} = \s{y}.Comment: 13 pages, 1 figur

    Some Physical Appearances of Vector Coherent States and CS Related to Degenerate Hamiltonians

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    In the spirit of some earlier work on the construction of vector coherent states over matrix domains, we compute here such states associated to some physical Hamiltonians. In particular, we construct vector coherent states of the Gazeau-Klauder type. As a related problem, we also suggest a way to handle degeneracies in the Hamiltonian for building coherent states. Specific physical Hamiltonians studied include a single photon mode interacting with a pair of fermions, a Hamiltonian involving a single boson and a single fermion, a charged particle in a three dimensional harmonic force field and the case of a two-dimensional electron placed in a constant magnetic field, orthogonal to the plane which contains the electron. In this last example, an interesting modular structure emerges for two underlying von Neumann algebras, related to opposite directions of the magnetic field. This leads to the existence of coherent states built out of KMS states for the system.Comment: 38 page

    Some Biorthogonal Families of Polynomials Arising in Noncommutative Quantum Mechanics

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    In this paper we study families of complex Hermite polynomials and construct deformed versions of them, using a GL(2,C)GL(2,\mathbb{C}) transformation. This construction leads to the emergence of biorthogonal families of deformed complex Hermite polynomials, which we then study in the context of a two-dimensional model of noncommutative quantum mechanics.Comment: 17 page

    Modelling stock volatilities during financial crises: A time varying coefficient approach

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    We examine how the most prevalent stochastic properties of key financial time series have been affected during the recent financial crises. In particular we focus on changes associated with the remarkable economic events of the last two decades in the volatility dynamics, including the underlying volatility persistence and volatility spillover structure. Using daily data from several key stock market indices, the results of our bivariate GARCH models show the existence of time varying correlations as well as time varying shock and volatility spillovers between the returns of FTSE and DAX, and those of NIKKEI and Hang Seng, which became more prominent during the recent financial crisis. Our theoretical considerations on the time varying modelwhich provides the platformupon which we integrate our multifaceted empirical approaches are also of independent interest. In particular, we provide the general solution for time varying asymmetric GARCH specifications, which is a long standing research topic. This enables us to characterize these models by deriving, first, their multistep ahead predictors, second, the first two time varying unconditional moments, and third, their covariance structure.Open Access funded by European Research Council under a Creative Commons license
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