Haye Hinrichsen

Maximal localization in the presence of minimal uncertainties in positions and in momenta

Small corrections to the uncertainty relations, with effects in the ultraviolet and/or infrared, have been discussed in the context of string theory and quantum gravity. Such corrections lead to small but finite minimal uncertainties in position and/or momentum measurements. It has been shown that these effects could indeed provide natural cutoffs in quantum field theory. The corresponding underlying quantum theoretical framework includes small ‘‘noncommutative geometric’’ corrections to the canonical commutation relations. In order to study the full implications on the concept of locality, it is crucial to find the physical states of then maximal localization. These states and their properties have been calculated for the case with minimal uncertainties in positions only. Here we extend this treatment, though still in one dimension, to the general situation with minimal uncertainties both in positions and in momenta.

ON MATRIX PRODUCT GROUND STATES FOR REACTION-DIFFUSION MODELS

We discuss a new mechanism leading to a matrix product form for the stationary state of one-dimensional stochastic models. The corresponding algebra is quadratic and involves four different matrices. For the example of a coagulation - decoagulation model explicit four-dimensional representations are given and exact expressions for various physical quantities are recovered. We also find the general structure of n-point correlation functions at the phase transition.

Matrix product ground states for exclusion processes with parallel dynamics

We show in the example of a one-dimensional asymmetric exclusion process that stationary states of models with parallel dynamics may be written in a matrix product form. The corresponding algebra is quadratic and involves three different matrices. Using this formalism we prove previous conjectures for the equal-time correlation functions of the model.

Roughening transition in a one-dimensional growth process.

A class of nonequilibrium models with short-range interactions and sequential updates is presented. The models describe one dimensional growth processes which display a roughening transition between a smooth and a rough phase. This transition is accompanied by spontaneous symmetry breaking, which is described by an order parameter whose dynamics is non-conserving. Some aspects of models in this class are related to directed percolation in 1+1 dimensions, although unlike directed percolation the models have no absorbing states. Scaling relations are derived and compared with Monte Carlo simulations.

DETERMINISTIC EXCLUSION PROCESS WITH A STOCHASTIC DEFECT : MATRIX-PRODUCT GROUND STATES

We study a one-dimensional anisotropic exclusion model describing particles moving deterministically on a ring with a single defect, across which they move with probability 0 < q < 1. We show that the stationary state of this model can be represented as a matrix-product state.

STOCHASTIC LATTICE MODELS WITH SEVERAL ABSORBING STATES

We study two models with n equivalent absorbing states that generalize the Domany-Kinzel cellular automaton and the contact process. Numerical investigations show that for n=2 both models belong to the same universality class as branching annihilating walks with an even number of offspring. Unlike previously known models, these models have no explicit parity conservation law.

AN ALGORITHM-INDEPENDENT DEFINITION OF DAMAGE SPREADING : APPLICATION TO DIRECTED PERCOLATION

We present a general definition of damage spreading in a pair of models. Using this general framework, one can define damage spreading in an objective manner that does not depend on the particular dynamic procedure that is being used. The formalism can be used for any spin-model or cellular automaton, with sequential or parallel update rules. At this point we present its application to the Domany–Kinzel cellular automaton in one dimension, this being the simplest model in which damage spreading has been found and studied extensively. We show that the active phase of this model consists of three subphases characterized by different damage-spreading properties.

Damage spreading in the Ising model

We present two interesting results regarding damage spreading in ferromagnetic Ising models. First, we show that a damage spreading transition can occur in an Ising chain that evolves in contact with a thermal reservoir. Damage heals at low temperature and spreads at high T. The dynamic rules for the system{close_quote}s evolution for which such a transition is observed are as legitimate as the conventional rules (Glauber, Metropolis, heat bath). Our second result is that such transitions are not always in the directed percolation universality class. {copyright} {ital 1997} {ital The American Physical Society}

Universality properties of the stationary states in the one-dimensional coagulation-diffusion model with external particle input

We investigate with the help of analytical and numerical methods the reactionA+A→A on a one-dimensional lattice opened at one end and with an input of particles at the other end. We show that if the diffusion rates to the left and to the right are equal, for largex, the particle concentrationc(x) behaves likeAsx−1 (x measures the distance to the input end). If the diffusion rate in the direction pointing away from the source is larger than the one corresponding to the opposite direction, the particle concentration behaves likeAax−1/2. The constantsAs andAa are independent of the input and the two coagulation rates. The universality ofAa comes as a surprise, since in the asymmetric case the system has a massive spectrum.

Wetting under nonequilibrium conditions.

We report a detailed account of the phase diagram of a recently introduced model for nonequilibrium wetting in (1+1) dimensions [H. Hinrichsen, R. Livi, D. Mukamel, and A. Politi, Phys. Rev. Lett. 79, 2710 (1997)]. A mean-field approximation is shown to reproduce the main features of the phase diagram, while providing indications for the behavior of the wetting transition in higher dimensions. The mean-field phase diagram is found to exhibit an extra transition line which does not exist in (1+1) dimensions. The line separates a phase in which the interface height distribution decays exponentially at large heights from a superexponentially decaying phase. Implications to wetting in dimensions higher than (1+1) are discussed.