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arXiv · 1902.07751

Generalized Gibbs Ensembles of the classical Toda chain

Herbert Spohn
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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. In the current version missing factors of 2 are corrected.

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BibTeXRIS

Herbert Spohn. 2019-02-20. Generalized Gibbs Ensembles of the classical Toda chain. https://doi.org/10.1007/s10955-019-02320-5

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