Hydrodynamic Scales of Integrable Many-Body Systems

图书简介

This book provides a broad introduction to integrable systems with many degrees of freedom. Within the much larger domain, there are well studied classical models such as Toda lattice, Calogero fluid, Ablowitz-Ladik discretized nonlinear Schrödinger equation, and Korteweg-de Vries equation. For quantum mechanical systems, there are the Lieb-Liniger delta-Bose gas and the quantum Toda fluid. The truly novel twist is the study of random initial data described by generalized Gibbs ensembles with parameters of slow spatial variation. This is the hydrodynamic scale, comparable to the ballistic Euler scale of simple fluids. While integrable microscopic models are very diverse, the central theme of this book is to elucidate their structural similarity on hydrodynamic scales.Key FeaturesSelf-contained introduction to the hydrodynamics of integrable many-particle systemsCovers classical and quantum many-body modelsElucidates common structural features300 references including many recent contributions

Preface; Overview; Dynamics of the Classical Toda Lattice: Locally Conserved Fields and Their Currents; Action-angle Variables, Notions of Integrability; Scattering Theory; Static Properties: Generalized Gibbs Ensembles; Lax Matrix Filter and Local GGEs; Generalized Free Energy; Lax Density of States, TBA Equation; Mean-Field Techniques; Dyson Brownian Motion; Hydrodynamics for Hard Rods; Equations of Generalized Hydrodynamics: Average Currents; Hydrodynamic Equations; Linearized Hydrodynamics and GGE Spacetime Correlations: Equilibrium Spacetime Correlations for Nonintegrable Chains; GGE Spacetime Correlations for the Toda Lattice; Domain Wall Initial States; Toda Fluid: Euler Equations; Generalized Free Energy — Again; Hydrodynamics of Soliton Gases: Soliton Gas of the Korteweg-de Vries Equation; Soliton Gas of the Toda Lattice; Comparing Soliton- and Particle-Based Hydrodynamics; Calogero Models: Hyperbolic Calogero Model, Charges and Currents; Scattering Coordinates; Generalized Free Energy; Classical Bethe Equations; Trigonometric Calogero-Moser Model; Discretized Nonlinear Schrödinger Equation: Continuum Wave Equations; Ablowitz-Ladik Discretization; Circular Random Matrices with Pressure Ramp; Average Currents, Hydrodynamic Equations; Modified Korteweg-de Vries Equation; Hydrodynamics for the Lieb-Liniger δ-Bose Gas: Bethe Ansatz; Bethe Root Densities, Free Energy, TBA Equations; Charge Currents, Hydrodynamic Equations; Generic Structure of TBA; Gaudin Matrix; Quantum Toda Lattice: Integrability, Monodromy Matrix; Spectral Properties; GGE and Hydrodynamics; Beyond the Euler Time Scale: General Framework; Nonintegrable Chains; Navier–Stokes Equations; Bibliography

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Hydrodynamic Scales of Integrable Many-Body Systems 可积多体系统的流体动力学尺度 凝聚态物理学

Hydrodynamic Scales of Integrable Many-Body Systems

可积多体系统的流体动力学尺度
凝聚态物理学