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Classical Toda lattice with domain wall initial conditions

by Christian B. Mendl, Herbert Spohn

Submission summary

As Contributors: Christian Mendl
Arxiv Link: (pdf)
Code repository:
Date submitted: 2020-12-17 13:28
Submitted by: Mendl, Christian
Submitted to: SciPost Physics
Academic field: Physics
  • Statistical and Soft Matter Physics
Approaches: Theoretical, Computational


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.

Current status:
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Submission 2011.11008v1 on 17 December 2020

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