Many Peoples, Many Faiths: Women and Men in the World Religions 2023 (11版)
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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.
原價:
3215
售價:
3054
現省:
161元
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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.
原價:
2417
售價:
2296
現省:
121元
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Many-Body Theory of Condensed Matter Systems
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In this primer to the many-body theory of condensed-matter systems, the authors introduce the subject to the non-specialist in a broad, concise, and up-to-date manner. A wide range of topics are covered including the second quantization of operators, coherent states, quantum-mechanical Green's functions, linear response theory, and Feynman diagrammatic perturbation theory. Material is also incorporated from quantum optics, low-dimensional systems such as graphene, and localized excitations in systems with boundaries as in nanoscale materials. Over 100 problems are included at the end of chapters, which are used both to consolidate concepts and to introduce new material. This book is suitable as a teaching tool for graduate courses and is ideal for non-specialist students and researchers working in physics, materials science, chemistry, or applied mathematics who want to use the tools of many-body theory.
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A Mind Over Matter: Philip Anderson and the Physics of the Very Many
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