Current fluctuations in the zero-range process with open boundaries

Condensation occurs in nonequilibrium steady states when a finite fraction of particles in the system occupies a single lattice site. We study condensation transitions in a one-dimensional zero-range process with a single defect site. The system is analysed in the grand canonical and canonical ensembles and the two are contrasted. Two distinct condensation mechanisms are found in the grand canonical ensemble. Discrepancies between the infinite and large but finite systems' pa...

The asymmetric simple exclusion process with open boundaries, which is a very simple model of out-of-equilibrium statistical physics, is known to be integrable. In particular, its spectrum can be described in terms of Bethe roots. The large deviation function of the current can be obtained as well by diagonalizing a modified transition matrix, that is still integrable: the spectrum of this new matrix can be also described in terms of Bethe roots for special values of the para...

We study the fluctuations of the current J(t) of the totally asymmetric exclusion process with open boundaries. Using a density matrix renormalization group approach, we calculate the cumulant generating function of the current. This function can be interpreted as a free energy for an ensemble in which histories are weighted by exp(-sJ(t)). We show that in this ensemble the model has a first order space-time phase transition at s=0. We numerically determine the finite size sc...

In this thesis, we consider one of the most popular models of non-equilibrium statistical physics: the Asymmetric Simple Exclusion Process, in which particles jump stochastically on a one-dimensional lattice, between two reservoirs at fixed densities, with the constraint that each site can hold at most one particle at a given time. This model has the mathematical property of being integrable, which makes it a good candidate for exact calculations. What interests us in particu...

We study the asymmetric exclusion process with open boundaries and derive the exact form of the joint probability function for the occupation number and the current through the system. We further consider the thermodynamic limit, showing that the resulting distribution is non-Gaussian and that the density fluctuations have a discontinuity at the continuous phase transition, while the current fluctuations are continuous. The derivations are performed by using the standard oper...

We numerically study the large deviation function of the total current, which is the sum of local currents over all bonds, for the symmetric and asymmetric simple exclusion processes with open boundary conditions. We estimate the generating function by calculating the largest eigenvalue of the modified transition matrix and by population Monte Carlo simulation. As a result, we find a number of interesting behaviors not observed in the exactly solvable cases studied previously...

Dynamical phase transitions are crucial features of the fluctuations of statistical systems, corresponding to boundaries between qualitatively different mechanisms of maintaining unlikely values of dynamical observables over long periods of time. They manifest themselves in the form of non-analyticities in the large deviation function of those observables. In this paper, we look at bulk-driven exclusion processes with open boundaries. It is known that the standard asymmetric ...

The dynamics of a class of zero-range processes exhibiting a condensation transition in the stationary state is studied. The system evolves in time starting from a random disordered initial condition. The analytical study of the large-time behaviour of the system in its mean-field geometry provides a guide for the numerical study of the one-dimensional version of the model. Most qualitative features of the mean-field case are still present in the one-dimensional system, both ...

We study spectral gaps of the one-dimensional totally asymmetric simple exclusion process (TASEP) with open boundaries in the maximal current phase. Earlier results for the model with periodic boundaries suggest that the gaps contributing to the universal KPZ regime may be understood as points on an infinite genus Riemann surface built from a parametric representation of the cumulant generating function of the current. We perform explicit analytic continuations from the known...

We consider the behaviour of current fluctuations in the one-dimensional partially asymmetric zero-range process with open boundaries. Significantly, we find that the distribution of large current fluctuations does not satisfy the Gallavotti-Cohen symmetry and that such a breakdown can generally occur in systems with unbounded state space. We also discuss the dependence of the asymptotic current distribution on the initial state of the system.