# Two-species hardcore reversible cellular automaton: matrix ansatz for dynamics and nonequilibrium stationary state

## TL;DR

This paper analyzes a reversible two-species cellular automaton's dynamics and stationary states using an exact matrix product approach, revealing phase-dependent transport behaviors.

## Contribution

It introduces an exact matrix product solution for the automaton's dynamics and stationary states, providing analytical insights into phase-dependent transport phenomena.

## Key findings

- Exact matrix product expressions for time evolution and stationary distribution
- Identification of phases with ballistic or diffusive transport
- Analytical density profiles and particle currents

## Abstract

In this paper we study the statistical properties of a reversible cellular automaton in two out-of-equilibrium settings. In the first part we consider two instances of the initial value problem, corresponding to the inhomogeneous quench and the local quench. Our main result is an exact matrix product expression of the time evolution of the probability distribution, which we use to determine the time evolution of the density profiles analytically. In the second part we study the model on a finite lattice coupled with stochastic boundaries. Once again we derive an exact matrix product expression of the stationary distribution, as well as the particle current and density profiles in the stationary state. The exact expressions reveal the existence of different phases with either ballistic or diffusive transport depending on the boundary parameters.