HYDRODYNAMIC SCALES OF INTEGRABLE MANY-BODY SYSTEMS

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The book explores integrable systems with multiple degrees of freedom, highlighting models like the classical Toda lattice and the quantum Toda lattice. It introduces a novel approach by examining random initial data through generalized Gibbs ensembles, focusing on hydrodynamic scales. The central theme emphasizes the structural similarities among diverse integrable microscopic particle models, drawing parallels to the ballistic Euler scale found in nonintegrable fluids. This comprehensive introduction bridges classical and quantum perspectives within the field.