Generalized hydrodynamics in box-ball systems
Grégoire Misguich (IPhT Saclay)
The box-ball system (BBS) is an integrable cellular automata introduced
in 1990 (Takahashi and J. Satsuma). This classical dynamical system
involves ‘balls’ placed in ‘boxes’ along on a line, and with simple
deterministic rules governing how the balls move at each time step. We
give an introduction to the simplest single-color BBS, focusing on the
properties its solitons. Next we will discuss a problem where the
initial state is a statistical ensemble of configurations with different
ball densities in the left and in the right halves of the system. With
the help of numerical simulations we show how the dynamics triggered by
such a domain-wall initial state leads to the emergence of density
plateaux. Using the generalized hydrodynamics framework we explain how
to compute analytically the large-time and large-distance properties of
these plateaux structures. If time permits the end of the presentation
will show some exact results concerning the fluctuations of the number
of balls crossing a given point (including large deviations) as well as
exact results on some current-current correlations (Drude weight).
References: A. Kuniba, G. Misguich and V. Pasquier, J. Phys A. 53,
404001(2020). See also: SciPost Phys. 10, 095 (2021) and J. Phys. A:
Math. Theor. 55 244006 (2022)