(特價書499 ) Modern Many-Particle Physics Atomic Gases, Quantum Dots and Quantum Fluids 2003

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書名：(特價 ) Modern Many-Particle Physics Atomic Gases, Quantum Dots and Quantum Fluids 2003 (WS) 981-238-346-8 作者：E.LIPPARINI 出版社：World Scientific 出版日期：2003-12 ISBN：9789812383464

Integrable Many-Particle Systems

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It is commonly known that three or more particles interacting via a two-body potential is an intractable problem. However, similar systems confined to one dimension yield exactly solvable equations, which have seeded widely pursued studies of one-dimensional n-body problems. The interest in these investigations is justified by their rich and quantitative insights into real-world classical and quantum problems, birthing a field that is the subject of this book. Spanning four bulk chapters, this book is written with the hope that readers come to appreciate the beauty of the mathematical results concerning the models of many-particle systems, such as the interaction between light particles and infinitely massive particles, as well as interacting quasiparticles. As the book discusses several unsolved problems in the subject, it functions as an insightful resource for researchers working in this branch of mathematical physics. In Chapter 1, the author first introduces readers to interesting problems in mathematical physics, with the prime objective of finding integrals of motion for classical many-particle systems as well as the exact solutions of the corresponding equations of motions. For these studied systems, their quantum mechanical analogue is then developed in Chapter 2. In Chapter 3, the book focuses on a quintessential problem in the quantum theory of magnetism: namely, to find all integrable one-dimensional systems involving quasiparticles of interacting one-half spins. Readers will study the integrable periodic chains of interacting one-half spins and discover the integrals of motion for such systems, as well as the eigenvectors of their corresponding Hamiltonians. In the last chapter, readers will study about integrable systems of quantum particles, with spin and mutual interactions involving rational, trigonometric, or elliptic potentials. Sample Chapter(s) Preface Chapter 1: Classical Systems Disconnected with Lie Algebras Contents: Classical Systems Disconnected with Lie Algebras Quantum Systems Integrable Systems of Quasi-particles Integrable Systems of Particles with Spin Readership: Researchers in the field of mathematical physics.

Hydrodynamic Scales of Integrable Many-Body Systems

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This book provides a broad introduction to integrable systems with many degrees of freedom. Within a much larger orbit, discussed are models such as the classical Toda lattice, Calogero fluid, and Ablowitz-Ladik discretized nonlinear Schrödinger equation. On the quantum mechanical side, featured are the Lieb-Liniger delta-Bose gas and the quantum Toda lattice. As a genuinely novel twist, the study deals with random initial data described by generalized Gibbs ensembles with parameters of slow spatial variation. This is the hydrodynamic scale, in spirit similar to the ballistic Euler scale of nonintegrable simple fluids. While integrable microscopic particle models are very diverse, the central theme of this book is to elucidate their structural similarity on hydrodynamic scales. Sample Chapter(s) Preface Chapter 1: Overview Contents: 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 Macroscopic Equation, Law of Large Numbers Fluctuation Theory Hydrodynamics for Hard Rods Hard Rod Fluid Hard Rod Lattice TBA, Collision Rate Ansatz 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 KdV 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 Hydrodynamic Equations 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 List of Symbols Index Readership: Theoretical physicists and mathematicians interested in integrable models with many degrees of freedom.