Generalized Gibbs Ensembles of the Classical Toda Chain

Herbert Spohn

doi:10.1007/s10955-019-02320-5

Generalized Gibbs Ensembles of the Classical Toda Chain

Herbert Spohn

TUM Emeriti of Excellence

Research output: Contribution to journal › Article › peer-review

58 Scopus citations

Abstract

The Toda chain is the prime example of a classical integrable system with strictly local conservation laws. Relying on the Dumitriu–Edelman matrix model, we obtain the generalized free energy of the Toda chain and thereby establish a mapping to the one-dimensional log-gas with an interaction strength of order 1 / N. The (deterministic) local density of states of the Lax matrix is identified as the object, which should evolve according to generalized hydrodynamics.

Original language	English
Pages (from-to)	4-22
Number of pages	19
Journal	Journal of Statistical Physics
Volume	180
Issue number	1-6
DOIs	https://doi.org/10.1007/s10955-019-02320-5
State	Published - 1 Sep 2020

Keywords

GGE free energy
Mean-field Dyson’s Brownian motion
Random Lax matrix
Toda chain

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Generalized Gibbs Ensembles of the Classical Toda Chain

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Keywords

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