Hydrodynamic scales of integrable many-body systems
type: Item
instance of: scholarly article
title: Hydrodynamic scales of integrable many-body systems
DOI: 10.1142/13600
author: Herbert Spohn
publication date: 2024-05-23T00:00:00Z
review text: The words ``hydrodynamic scales'' in the title suggests that this is a study of fluids and their motions. Instead, in this book the author considers the subject in a much broader context, and describes it as based on the ``observation that the motion of a large assembly of strongly interacting particles is constrained by local conservation laws''. The author's intention is to provide an introduction to integrable systems with many degrees of freedom. Indeed, the author states in his overview that all integrable multi-particle systems are structurally alike on a hydrodynamic scale.\N\NGeneralized hydrodynamics is concerned with integrable many particle models where the number of conserved fields is proportional to system size.\N\NThe author begins by establishing the Toda lattice as a guiding backbone, one that is peculiar because it is integrable for every system size, and suggests that the conventional definition of integrability might need to be reconsidered, especially in the sense that the usual definition of integrability for quantum systems fails. He suggests that -- for hydrodynamic considerations -- a system should be called integrable if it has an infinite number of linearly independent local conservation laws.\N\NBesides the Toda lattice, the author examines models for the Dyson Brownian motion, a fluid system with hot rods, Calogero fluids, and the Ablowitz-Ladik discretized nonlinear Schrödinger equation.\N\NThe Toda lattice helps provide a guiding theme, in part because it shares the dynamical features of the Korteweg-deVries equation and the Toda fluid, then later leads to considerations of the quantum mechanical Lieb-Liniger delta-Bose gas and the quantum Toda lattice. The author also deals with random initial data described by generalized Gibbs ensembles with parameters of slow spatial variation. This hydrodynamic scale, as he says, should be understood in the context of the ballistic Euler scale.\N\NIntegrable microscopic particle models are truly v…
reviewed by: William J. Satzer Jr.
Mathematics Subject Classification ID: 37-02
Mathematics Subject Classification ID: 82-02
Mathematics Subject Classification ID: 37J35
Mathematics Subject Classification ID: 37K10
Mathematics Subject Classification ID: 37K60
Mathematics Subject Classification ID: 39A36
Mathematics Subject Classification ID: 70H06
Mathematics Subject Classification ID: 70F45
Mathematics Subject Classification ID: 82B23
Mathematics Subject Classification ID: 76M28
zbMATH DE Number: 7852571
zbMATH Keywords: integrable systems
zbMATH Keywords: many degrees of freedom
zbMATH Keywords: Toda lattice
zbMATH Keywords: Calogero fluid
zbMATH Keywords: Ablowitz-Ladik discretized Schrödinger equation
zbMATH Keywords: hydrodynamic scale
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 7852571