Soliton Solution for a Particle in One-Dimensional Periodic Box

ANJALI JANGID, Pooja Devi, Aniruddha Chakraborty

ANJALI JANGID, Pooja Devi, Harsh Soni +1 more

Andrzej Syrwid, Krzysztof Sacha

The Schr\"odinger equation for a Bose gas with repulsive contact interactions in a one-dimensional space may be solved analytically with the help of the Bethe ansatz if we impose periodic boundary conditions. It was shown that for such a system there exist many-body eigenstates directly corresponding to dark soliton solutions of the mean-field equation. The system is still integrable if one switches from the periodic boundary conditions to an infinite-square-well potential. The corresponding eigenstates were constructed by Gaudin. We analyze the weak-interaction limit of Gaudin's solutions and identify the parametrization of eigenstates strictly connected with single and multiple dark solitons. Numerical simulations of measurements of the particles' positions reveal dark solitons in the weak-interaction regime and their quantum nature in the presence of strong interactions.

N. I. Kislukha, В. И. Пономаренко

Atsuo Kuniba, Grégoire Misguich, Vincent Pasquier

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.

Kazumi Maki