Regensburg 2022 – wissenschaftliches Programm

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DY: Fachverband Dynamik und Statistische Physik

DY 49: Statistical Physics: General

DY 49.9: Vortrag

Freitag, 9. September 2022, 11:45–12:00, H20

Generalized hydrodynamics description of the classical Toda lattice and high-low pressure domain wall initial conditions — •Christian Mendl and Herbert Spohn — Technische Universität München (TUM)

We review and discuss generalized hydrodynamics applied to the classical Toda lattice, a paradigmatic example for an interacting integrable system. One first identifies the Lax matrix of the system, which is closely related to the microscopic conservation laws. For the Toda lattice, the free energy can be expressed in terms of the eigenvalue spectrum of the Lax matrix. One finally arrives at semi-analytic formulas for dynamical correlation functions in equilibrium, which show good agreement with molecular dynamic simulations.

In the second part, we focus on domain wall initial conditions, for which the left and right half lattice are in thermal equilibrium but with distinct parameters. The particular case of interest is a jump from low to high pressure at uniform temperature and zero mean velocity, whereby the scaling function for the average stretch is forced to change sign. The hydrodynamic equations seem to be singular at zero stretch, but nevertheless the self-similar solution exhibits smooth behavior.

[1] C. B. Mendl, H. Spohn, High-low pressure domain wall for the classical Toda lattice, SciPost Phys. Core 5, 002 (2022)

[2] H. Spohn, Hydrodynamic equations for the Toda lattice, arXiv:2101.06528

[3] H. Spohn, Generalized Gibbs ensembles of the classical Toda chain, J. Stat. Phys. 180, 4 (2020)