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Elephants can always remember: exact long-range memory effects in a non-Markovian random walk.
We consider a discrete-time random walk where the random increment at time step t depends on the full history of the process. We calculate exactly the mean and variance of the position and discuss
Phase transitions in an exactly soluble one-dimensional exclusion process
We consider an exclusion process with particles injected with rate α at the origin and removed with rate β at the right boundary of a one-dimensional chain of sites. The particles are allowed to hop
Duality relations for asymmetric exclusion processes
We derive duality relations for a class ofUq[SU(2)]-symmetric stochastic processes, including among others the asymmetric exclusion process in one dimension. Like the known duality relations for
Phase diagram of one-dimensional driven lattice gases with open boundaries
We consider the asymmetric simple exclusion process (ASEP) with open boundaries and other driven stochastic lattice gases of particles entering, hopping and leaving a one- dimensional lattice. The
Condensation in the Zero Range Process: Stationary and Dynamical Properties
The zero range process is of particular importance as a generic model for domain wall dynamics of one-dimensional systems far from equilibrium. We study this process in one dimension with rates which
Current Distribution and Random Matrix Ensembles for an Integrable Asymmetric Fragmentation Process
We calculate the time-evolution of a discrete-time fragmentation process in which clusters of particles break up and reassemble and move stochastically with size-dependent rates. In the
Transport in the XX chain at zero temperature: emergence of flat magnetization profiles.
The states emerging in the scaling limit are compared to those of a homogeneous system where the same magnetization current is driven by a bulk field, and it is found that the expectation values of various quantities agree in the two systems.
Real-time dynamics in spin-1/2 chains with adaptive time-dependent density matrix renormalization group.
It is found that the error at small times is dominated by the error made by the Trotter decomposition, whereas for longer times the DMRG truncation error becomes the most important, with a very sharp crossover at some "runaway" time.
Localization of shocks in driven diffusive systems without particle number conservation.
The existence of a localized double density shock is demonstrated in one-dimensional driven diffusive systems and the hydrodynamic equations that describe the density profile in systems with uncorrelated steady state as well as in those exhibiting correlations.