4,205 research outputs found

    A novel Recurrence-Transience transition and Tracy-Widom growth in a cellular automaton with quenched noise

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    We study the growing patterns formed by a deterministic cellular automaton, the rotor-router model, in the presence of quenched noise. By the detailed study of two cases, we show that: (a) the boundary of the pattern displays KPZ fluctuations with a Tracy-Widom distribution, (b) as one increases the amount of randomness, the rotor-router path undergoes a transition from a recurrent to a transient walk. This transition is analysed here for the first time, and it is shown that it falls in the 3D Anisotropic Directed Percolation universality class.Comment: 6 pages + 8 pages SI, updated version with some correction

    A class of exactly solved assisted hopping models of active-absorbing state transitions on a line

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    We construct a class of assisted hopping models in one dimension in which a particle can move only if it does not lie in an otherwise empty interval of length greater than n+1n+1. We determine the exact steady state by a mapping to a gas of defects with only on-site interaction. We show that this system undergoes a phase transition as a function of the density ρ\rho of particles, from a low-density phase with all particles immobile for ρρc=1n+1\rho \le \rho_c = \frac{1}{n+1}, to an active state for ρ>ρc\rho > \rho_c. The mean fraction of movable particles in the active steady state varies as (ρρc)β(\rho - \rho_c)^{\beta}, for ρ\rho near ρc\rho_c. We show that for the model with range nn, the exponent β=n\beta =n, and thus can be made arbitrarily large.Comment: 4 page

    Poles in the SS-Matrix of Relativistic Chern-Simons Matter theories from Quantum Mechanics

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    An all orders formula for the SS-matrix for 2 \rightarrow 2 scattering in large N Chern-Simons theory coupled to a fundamental scalar has recently been conjectured. We find a scaling limit of the theory in which the pole in this SS-matrix is near threshold. We argue that the theory must be well described by non-relativistic quantum mechanics in this limit, and determine the relevant Schroedinger equation. We demonstrate that the SS-matrix obtained from this Schroedinger equation agrees perfectly with this scaling limit of the relativistic SS-matrix; in particular the pole structures match exactly. We view this matching as a nontrivial consistency check of the conjectured field theory SS-matrix.Comment: 12 pages, minor correction