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Friday, August 23, 2019 - 14:00 in ZiF

Hydrodynamics of the classical Toda chain and random matrix theory

A talk in the Summer School Randomness in Physics & Mathematics series by
Herbert Spohn

Abstract: There has been a lot of interest, mostly on the quantum side, to develop the hydrodynamics of integrable systems, thus involving an in nite number of conservation laws. Surprisingly a model-independent structure is claimed, except for the speci c two-particle phase shift. I will use the classical Toda chain as a road map for the general picture. The Toda chain has a tridiagonal Lax matrix, which under the generalised Gibbs ensemble becomes random. The corresponding density of states can be determined through a tricky use of the Dumitriu-Edelman theorem. Also a connection to Dyson's Brownian motion will be discussed.


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