Abstract
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 space-time profiles scale ballisticly. The particular case of interest is a jump from low to high pressure at uniform temperature and zero mean velocity. Thereby the scaling function for the average stretch (also free volume) is forced to change sign. By direct inspection, the hydrodynamic equations for the Toda lattice seem to be singular at zero stretch. In our contribution we report on numerical solutions and convincingly establish that nevertheless the self-similar solution exhibits smooth behavior.
Highlights
Over the past decade the out-of-equilibrium dynamics of many-body systems in one dimension has received a lot of attention, see for example the recent survey article [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
The hydrodynamic equations for the Toda lattice seem to be singular at zero stretch
Summary
Over the past decade the out-of-equilibrium dynamics of many-body systems in one dimension has received a lot of attention, see for example the recent survey article [1]. A further much studied choice, the one discussed in our contribution, is domain wall: In the left/right half lattice one prepares thermal states of a given translation invariant hamiltonian. In the position-(spectral parameter) plane one has to determine a contact line at which the spectral parameter jumps from its left to its right value This contact line fully characterizes the solution, which brings us to a second motivation for our study. While the entire self-similar solution of generalized hydrodynamics is computed numerically, most commonly only the spatial dependence of density, momentum, and temperature are displayed. Rather than such low order moments, we regard the contact line as more informative and will numerically determine its shape.
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