Exact Joint Density-Current Probability Function for the Asymmetric Exclusion Process

Exact joint density-current probability function for the asymmetric exclusion process.

We study the asymmetric simple 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 cur...

Formulas for joint probabilities for the asymmetric simple exclusion process

In earlier work, the authors Tracy, C. A. and Widom, H., “Integral formulas for the asymmetric simple exclusion process,” Commun. Math. Phys. 279, 815 2008 obtained integral formulas for probabilities for a single particle in the asymmetric simple exclusion process. Here, formulas are obtained for joint probabilities for several particles. In the case of a single particle, the derivation here i...

Exact relaxation dynamics in the totally asymmetric simple exclusion process.

The relaxation dynamics of the one-dimensional totally asymmetric simple exclusion process on a ring is considered in the case of step initial condition. Analyzing the time evolution of the local particle densities and currents by the Bethe ansatz method, we examine their full relaxation dynamics. As a result, we observe peculiar behaviors, such as the emergence of a ripple in the density profi...

Current Fluctuations for the Totally Asymmetric Simple Exclusion Process

The time-integrated current of the TASEP has non-Gaussian fluctuations of order t. The recently discovered connection to random matrices and the Painlevé II RiemannHilbert problem provides a technique through which we obtain the probability distribution of the current fluctuations, in particular their dependence on initial conditions, and the stationary two-point function. Some open problems ar...

Current Fluctuations for the Totally Asymmetric Simple Exclusion Process