2,386 research outputs found

    Driving particle current through narrow channels using classical pump

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    We study a symmetric exclusion process in which the hopping rates at two chosen adjacent sites vary periodically in time and have a relative phase difference. This mimics a colloidal suspension subjected to external space and time dependent modulation of the diffusion constant. The two special sites act as a classical pump by generating an oscillatory current with a nonzero DC{\cal DC} value whose direction depends on the applied phase difference. We analyze various features in this model through simulations and obtain an expression for the DC\cal{DC} current via a novel perturbative treatment.Comment: Revised versio

    Percolation Systems away from the Critical Point

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    This article reviews some effects of disorder in percolation systems even away from the critical density p_c. For densities below p_c, the statistics of large clusters defines the animals problem. Its relation to the directed animals problem and the Lee-Yang edge singularity problem is described. Rare compact clusters give rise to Griffiths singuraties in the free energy of diluted ferromagnets, and lead to a very slow relaxation of magnetization. In biassed diffusion on percolation clusters, trapping in dead-end branches leads to asymptotic drift velocity becoming zero for strong bias, and very slow relaxation of velocity near the critical bias field.Comment: Minor typos fixed. Submitted to Praman

    Supergrassmannian and large N limit of quantum field theory with bosons and fermions

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    We study a large N_{c} limit of a two-dimensional Yang-Mills theory coupled to bosons and fermions in the fundamental representation. Extending an approach due to Rajeev we show that the limiting theory can be described as a classical Hamiltonian system whose phase space is an infinite-dimensional supergrassmannian. The linear approximation to the equations of motion and the constraint yields the 't Hooft equations for the mesonic spectrum. Two other approximation schemes to the exact equations are discussed.Comment: 24 pages, Latex; v.3 appendix added, typos corrected, to appear in JM

    Determinant solution for the Totally Asymmetric Exclusion Process with parallel update

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    We consider the totally asymmetric exclusion process in discrete time with the parallel update. Constructing an appropriate transformation of the evolution operator, we reduce the problem to that solvable by the Bethe ansatz. The non-stationary solution of the master equation for the infinite 1D lattice is obtained in a determinant form. Using a modified combinatorial treatment of the Bethe ansatz, we give an alternative derivation of the resulting determinant expression.Comment: 34 pages, 5 figures, final versio

    One-Dimensional Directed Sandpile Models and the Area under a Brownian Curve

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    We derive the steady state properties of a general directed ``sandpile'' model in one dimension. Using a central limit theorem for dependent random variables we find the precise conditions for the model to belong to the universality class of the Totally Asymmetric Oslo model, thereby identifying a large universality class of directed sandpiles. We map the avalanche size to the area under a Brownian curve with an absorbing boundary at the origin, motivating us to solve this Brownian curve problem. Thus, we are able to determine the moment generating function for the avalanche-size probability in this universality class, explicitly calculating amplitudes of the leading order terms.Comment: 24 pages, 5 figure

    Dynamics at a smeared phase transition

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    We investigate the effects of rare regions on the dynamics of Ising magnets with planar defects, i.e., disorder perfectly correlated in two dimensions. In these systems, the magnetic phase transition is smeared because static long-range order can develop on isolated rare regions. We first study an infinite-range model by numerically solving local dynamic mean-field equations. Then we use extremal statistics and scaling arguments to discuss the dynamics beyond mean-field theory. In the tail region of the smeared transition the dynamics is even slower than in a conventional Griffiths phase: the spin autocorrelation function decays like a stretched exponential at intermediate times before approaching the exponentially small equilibrium value following a power law at late times.Comment: 10 pages, 8eps figures included, final version as publishe

    Explicit characterization of the identity configuration in an Abelian Sandpile Model

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    Since the work of Creutz, identifying the group identities for the Abelian Sandpile Model (ASM) on a given lattice is a puzzling issue: on rectangular portions of Z^2 complex quasi-self-similar structures arise. We study the ASM on the square lattice, in different geometries, and a variant with directed edges. Cylinders, through their extra symmetry, allow an easy determination of the identity, which is a homogeneous function. The directed variant on square geometry shows a remarkable exact structure, asymptotically self-similar.Comment: 11 pages, 8 figure

    Rolling tachyon solution of two-dimensional string theory

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    We consider a classical (string) field theory of c=1c=1 matrix model which was developed earlier in hep-th/9207011 and subsequent papers. This is a noncommutative field theory where the noncommutativity parameter is the string coupling gsg_s. We construct a classical solution of this field theory and show that it describes the complete time history of the recently found rolling tachyon on an unstable D0 brane.Comment: 19 pages, 2 figures, minor changes in text and additional references, correction of decay time (version to appear in JHEP.

    From Gravitons to Giants

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    We discuss exact quantization of gravitational fluctuations in the half-BPS sector around AdS5×_5 \times S5^5 background, using the dual super Yang-Mills theory. For this purpose we employ the recently developed techniques for exact bosonization of a finite number NN of fermions in terms of NN bosonic oscillators. An exact computation of the three-point correlation function of gravitons for finite NN shows that they become strongly coupled at sufficiently high energies, with an interaction that grows exponentially in NN. We show that even at such high energies a description of the bulk physics in terms of weakly interacting particles can be constructed. The single particle states providing such a description are created by our bosonic oscillators or equivalently these are the multi-graviton states corresponding to the so-called Schur polynomials. Both represent single giant graviton states in the bulk. Multi-particle states corresponding to multi-giant gravitons are, however, different, since interactions among our bosons vanish identically, while the Schur polynomials are weakly interacting at high enough energies.Comment: v2-references added, minor changes and typos corrected; 24 pages, latex, 3 epsf figure

    Relating Physical Observables in QCD without Scale-Scheme Ambiguity

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    We discuss the St\"uckelberg-Peterman extended renormalization group equations in perturbative QCD, which express the invariance of physical observables under renormalization-scale and scheme-parameter transformations. We introduce a universal coupling function that covers all possible choices of scale and scheme. Any perturbative series in QCD is shown to be equivalent to a particular point in this function. This function can be computed from a set of first-order differential equations involving the extended beta functions. We propose the use of these evolution equations instead of perturbative series for numerical evaluation of physical observables. This formalism is free of scale-scheme ambiguity and allows a reliable error analysis of higher-order corrections. It also provides a precise definition for ΛMS\Lambda_{\overline{\rm MS}} as the pole in the associated 't Hooft scheme. A concrete application to R(e+ehadrons)R(e^+e^- \to {\rm hadrons}) is presented.Comment: Plain TEX, 4 figures (available upon request), 22 pages, DOE/ER/40322-17
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