4,205 research outputs found

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

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

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 $n+1$. 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 $\rho$ of particles,
from a low-density phase with all particles immobile for $\rho \le \rho_c =
\frac{1}{n+1}$, to an active state for $\rho > \rho_c$. The mean fraction of
movable particles in the active steady state varies as $(\rho -
\rho_c)^{\beta}$, for $\rho$ near $\rho_c$. We show that for the model with
range $n$, the exponent $\beta =n$, and thus can be made arbitrarily large.Comment: 4 page

### Poles in the $S$-Matrix of Relativistic Chern-Simons Matter theories from Quantum Mechanics

An all orders formula for the $S$-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
$S$-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 $S$-matrix obtained from this
Schroedinger equation agrees perfectly with this scaling limit of the
relativistic $S$-matrix; in particular the pole structures match exactly. We
view this matching as a nontrivial consistency check of the conjectured field
theory $S$-matrix.Comment: 12 pages, minor correction

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