Generalized hydrodynamics of box-ball systems

by Prof. Atsuo Kuniba (University of Tokyo)

Thursday 12 Mar 2020, 11:00 → 12:00 Europe/Stockholm

132:028 (Nordita East)

Box-ball system (BBS) is a distinguished example of integrable
cellular automata in one dimension.
Its integrability has been studied extensively from the viewpoint of
quantum groups, Bethe ansatz,
ultradiscretization and tropical geometry. In this talk I introduce
the generalized Gibbs ensemble of
BBS soliton gas and present several results related to thermodynamic
Bethe ansatz and generalized hydrodynamics.
They include the limit shape problem of soliton distributions, the
solution to the speed equation for solitons and
its connection to the period matrix of  the tropical Riemann theta
function appearing in the Jacobi inversion problem of BBS,
an explicit description of the density plateaux that emerge from a
domain wall initial condition, as long as the time permits.
(Joint work with Grégoire Misguich and Vincent Pasquier.)