The box-ball system (BBS) is an integrable cellular automata introduced in 1990 [Takahashi & J. Satsuma]. It is a dynamical system where 'balls' occupy 'boxes' placed on a line, and with simple deterministic rules specifying how the balls move at each time step. We will start with an introduction to the simplest single-color BBS, focusing on the properties its solitons. Next we will present a setup where the initial state is a statistical ensemble of configurations with two different ball densities in the left and in the right halves of the system. With the help of numerical simulations we will show how the dynamics triggered by such a domain-wall initial state leads to the formation of density plateaux. Using the generalized hydrodynamics approach, including diffusive corrections, we will explain how to compute analytically several large-time and large-distance properties of these plateaux structures.
References: A. Kuniba, G. Misguich and V. Pasquier, J. Phys A. 53, 404001(2020) and SciPost Phys. 10, 095 (2021).
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