Generalized hydrodynamics in box-ball system
Atsuo Kuniba, Grégoire Misguich, Vincent Pasquier
Abstract
Abstract Box-ball system (BBS) is a prominent example of integrable cellular automata in one dimension connected to quantum groups, Bethe ansatz, ultradiscretization, tropical geometry and so forth. In this paper we study the generalized Gibbs ensemble of BBS soliton gas by thermodynamic Bethe ansatz and generalized hydrodynamics. The results include the solution to the speed equation for solitons, an intriguing connection of the effective speed with the period matrix of the tropical Riemann theta function, an explicit description of the density plateaux that emerge from domain wall initial conditions including their diffusive corrections.
Topics & Concepts
Bethe ansatzIntegrable systemCellular automatonAnsatzRiemann hypothesisPhysicsBall (mathematics)Mathematical physicsConnection (principal bundle)QuantumMathematicsClassical mechanicsMathematical analysisQuantum mechanicsGeometryAlgorithmAlgebraic structures and combinatorial modelsQuantum many-body systemsBlack Holes and Theoretical Physics