Classical Toda lattice with domain wall initial conditions

Christian B. Mendl, Herbert Spohn

Published 2020-11-22Version 1

We study the classical Toda lattice with domain wall initial conditions, for which left and right half lattice are in thermal equilibrium but with distinct parameters of pressure, mean velocity, and temperature. In the hydrodynamic regime the respective spacetime profiles scale ballistically. For a particular range of parameters one observes a huge peak in the particle density. We study this phenomenon on the basis of generalized hydrodynamics. While the density diverges as $1/|x|$, with a different choice of coordinates smooth behavior is recovered.