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Exact solution of a 1d asymmetric exclusion model using a matrix formulation
Several recent works have shown that the one-dimensional fully asymmetric exclusion model, which describes a system of particles hopping in a preferred direction with hard core interactions, can be
TOPICAL REVIEW: Nonequilibrium steady states of matrix-product form: a solver's guide
TLDR
The general problem of determining the steady state of stochastic nonequilibrium systems such as those used to model biological transport and traffic flow is considered, and a unified, pedagogical account of the various means by which the statistical mechanical calculations of macroscopic physical quantities are actually performed is presented.
Diffusion with stochastic resetting.
We study simple diffusion where a particle stochastically resets to its initial position at a constant rate r. A finite resetting rate leads to a nonequilibrium stationary state with non-Gaussian
Nonequilibrium statistical mechanics of the zero-range process and related models
We review recent progress on the zero-range process, a model of interacting particles which hop between the sites of a lattice with rates that depend on the occupancy of the departure site. We
Phase transitions in one-dimensional nonequilibrium systems
The phenomenon of phase transitions in one-dimensional systems is discussed. Equilibrium systems are reviewed and some properties of an energy function which may allow phase transitions and phase
Stochastic resetting and applications
In this Topical Review we consider stochastic processes under resetting, which have attracted a lot of attention in recent years. We begin with the simple example of a diffusive particle whose
Exact solution of a partially asymmetric exclusion model using a deformed oscillator algebra
We study the partially asymmetric exclusion process with open boundaries. We generalize the matrix approach previously used to solve the special case of total asymmetry and derive exact expressions
Glassy Time-Scale Divergence and Anomalous Coarsening in a Kinetically Constrained Spin Chain
We analyse the out of equilibrium behavior of an Ising spin chain with an asymmetric kinetic constraint after a quench to a low temperature T. In the limit T\to 0, we provide an exact solution of the
Diffusion with optimal resetting
We consider the mean time to absorption by an absorbing target of a diffusive particle with the addition of a process whereby the particle is reset to its initial position with rate r. We consider
Shock formation in an exclusion process with creation and annihilation.
TLDR
It is shown how the continuum mean-field equations can be studied analytically and hence derive the phase diagrams of the model and the stationary distribution of shock positions is calculated, by virtue of which the numerically determined finite-size scaling behavior of the shock width is explained.
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