Introduction To The Statistical Physics Of Integrable Many Body Systems

Author: Ladislav Šamaj
Publisher: Cambridge University Press
ISBN: 1107067669
Size: 19.61 MB
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Including topics not traditionally covered in literature, such as (1+1)-dimensional QFT and classical 2D Coulomb gases, this book considers a wide range of models and demonstrates a number of situations to which they can be applied. Beginning with a treatise of nonrelativistic 1D continuum Fermi and Bose quantum gases of identical spinless particles, the book describes the quantum inverse scattering method and the analysis of the related Yang–Baxter equation and integrable quantum Heisenberg models. It also discusses systems within condensed matter physics, the complete solution of the sine-Gordon model and modern trends in the thermodynamic Bethe ansatz. Each chapter concludes with problems and solutions to help consolidate the reader's understanding of the theory and its applications. Basic knowledge of quantum mechanics and equilibrium statistical physics is assumed, making this book suitable for graduate students and researchers in statistical physics, quantum mechanics and mathematical and theoretical physics.

Quantum Many Body Systems In One Dimension

Author: Zachary N C Ha
Publisher: World Scientific
ISBN: 9814500372
Size: 14.89 MB
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The main theme of the book is the intimate connection between the two families of exactly solvable models: the inverse-square exchange (ISE) and the nearest-neighbor exchange (NNE) models. The latter are better known as the Bethe-Ansatz solvable models and include the Heisenberg spin chain, t–J models and Hubbard models. The former, the Calogero–Sutherland family of models, are simple to solve and contain essentially the same physics as the NNE family. The author introduces and discusses current topics, such as the Luttinger liquid concept, fractional statistics, and spin–charge separation, in the context of the explicit models. Contents:IntroductionHeisenberg Spin ChainThe 1D Hubbard ModelModels with Inverse-Square ExchangeStrings in Long-Range Interaction ModelElementary Excitations of t-J ModelFractional Statistics in One-Dimension: View from an Exactly Solvable ModelConcluding Remarks Readership: Graduate students, researchers in statistical mechanics, mathematical physics and condensed matter physics. keywords:Quantum;Many-Body;One;Inverse Square;Exchange;Luttinger;Fractional Statistics

Back Of The Envelope Quantum Mechanics

Author: Maxim Olshanii
Publisher: World Scientific
ISBN: 9814508489
Size: 67.70 MB
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Dimensional and order-of-magnitude estimates are practiced by almost everybody but taught almost nowhere. When physics students engage in their first theoretical research project, they soon learn that exactly solvable problems belong only to textbooks, that numerical models are long and resource consuming, and that “something else” is needed to quickly gain insight into the system they are going to study. Qualitative methods are this “something else”, but typically, students have never heard of them before. The aim of this book is to teach the craft of qualitative analysis using a set of problems, some with solutions and some without, in advanced undergraduate and beginning graduate Quantum Mechanics. Examples include a dimensional analysis solution for the spectrum of a quartic oscillator, simple WKB formulas for the matrix elements of a coordinate in a gravitational well, and a three-line-long estimate for the ionization energy of atoms uniformly valid across the whole periodic table. The pièce de résistance in the collection is a series of dimensional analysis questions in Integrable Nonlinear Partial Differential Equations with no dimensions existing a priori. Solved problems include the relationship between the size and the speed of solitons of the Korteweg–de Vries equation and an expression for the oscillation period of a Nonlinear Schrödinger breather as a function of its width. Contents:Ground State Energy of a Hybrid Harmonic-Quartic Oscillator: A Case StudyBohr-Sommerfeld Quantization“Halved” Harmonic Oscillator: A Case StudySemi-Classical Matrix Elements of Observables and Perturbation TheoryVariational ProblemsGravitational Well: A Case StudyMiscellaneousThe Hellmann-Feynman TheoremLocal Density Approximation TheoriesIntegrable Partial Differential Equations Readership: Advanced undergraduate and beginning graduate students in physics. Keywords:Quantum Mechanics;WKB;Semi-Classical;Bohr–Sommerfeld Quantization;Perturbation Theory;Order of Magnitude;Dimensional Analysis;Back-of-the-Envelope;Integrable Nonlinear Partial Differential Equations;Solitons;Breathers;Nonlinear Schrödinger Equation;Korteweg–de Vries Equation;Sine–Gordon Equation;Kadomtsev–Petviashvili Equation;Lieb–Liniger Model;Calogero Model;Hellmann–Feynman Theorem;Virial Theorem;Calculus of VariationsKey Features:This book is the only existing title on qualitative methods in Quantum Mechanics at the advanced undergraduate / beginning graduate level. A B Migdal's Qualitative Methods in Quantum Theory (Westview Press (2000)) is far too advanced. M Gitterman and V Halpern's Qualitative Analysis of Physical Problems (Academic Press (1981)) is too broad. [Sanjoy Mahajan's, Street-Fighting Mathematics (The MIT Press (2010)) is on mathematics. Vladimir P Krainov's Qualitative Methods in Physical Kinetics and Hydrodynamics (American Institute of Physics (1992)) is on physical kinetics and hydrodynamics. The above list is likely to exhaust all the textbooks in qualitative methods in physics and mathematics ever publishedThe book is structured as a coherent sequence of problems aimed at addressing the whole spectrum of dimensional and order-of-magnitude methodsThis book can be used as a secondary text and a source for homework assignments in any advanced undergraduate / beginning graduate course in Quantum Mechanics or in Partial Differential Equations

A Kinetic View Of Statistical Physics

Author: Pavel L. Krapivsky
Publisher: Cambridge University Press
ISBN: 1139493345
Size: 63.64 MB
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Aimed at graduate students, this book explores some of the core phenomena in non-equilibrium statistical physics. It focuses on the development and application of theoretical methods to help students develop their problem-solving skills. The book begins with microscopic transport processes: diffusion, collision-driven phenomena, and exclusion. It then presents the kinetics of aggregation, fragmentation and adsorption, where the basic phenomenology and solution techniques are emphasized. The following chapters cover kinetic spin systems, both from a discrete and a continuum perspective, the role of disorder in non-equilibrium processes, hysteresis from the non-equilibrium perspective, the kinetics of chemical reactions, and the properties of complex networks. The book contains 200 exercises to test students' understanding of the subject. A link to a website hosted by the authors, containing supplementary material including solutions to some of the exercises, can be found at www.cambridge.org/9780521851039.

Many Body Physics Topology And Geometry

Author: Siddhartha Sen
Publisher: World Scientific
ISBN: 981467818X
Size: 32.17 MB
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The book explains concepts and ideas of mathematics and physics that are relevant for advanced students and researchers of condensed matter physics. With this aim, a brief intuitive introduction to many-body theory is given as a powerful qualitative tool for understanding complex systems. The important emergent concept of a quasiparticle is then introduced as a way to reduce a many-body problem to a single particle quantum problem. Examples of quasiparticles in graphene, superconductors, superfluids and in a topological insulator on a superconductor are discussed. The mathematical idea of self-adjoint extension, which allows short distance information to be included in an effective long distance theory through boundary conditions, is introduced through simple examples and then applied extensively to analyse and predict new physical consequences for graphene. The mathematical discipline of topology is introduced in an intuitive way and is then combined with the methods of differential geometry to show how the emergence of gapless states can be understood. Practical ways of carrying out topological calculations are described. Contents:OverviewMany-Body TheoryTopology and GeometryBoundary Conditions and Self-Adjoint ExtensionsElectronic Properties of Graphene Readership: Graduate students and researchers in condensed matter physics and mathematical physics. Key Features:Topics are of current interest, e.g. graphene, topological insulators, Majorana fermionsIs self-contained and provides all the background material necessary to understand the physical or mathematical concepts discussedPractical ways of using topology, self-adjoint extensions as well as ways of making qualitative estimates in physics are explained and then illustrated by examplesKeywords:Condensed Matter Physics;Topology;Differential Geometry;Many-Body Problem;Graphene;Self-Adjoint Extensions;K-Theory;Quasiparticles;Superconductivity;Superfluidity;Topological Insulator;Mathematical Physics

New Developments Of Integrable Systems And Long Ranged Interaction Models

Author: Ge Mo-lin
Publisher: World Scientific
ISBN: 9814549754
Size: 48.94 MB
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This textbook, pitched at the advanced-undergraduate to beginning-graduate level, focuses on mathematical topics of relevance in contemporary physics that are not usually covered in texts at the same level. Its main purpose is to help students appreciate and take advantage of the modern trend of very productive symbiosis between physics and mathematics. Three major areas are covered: (1) linear operators; (2) group representations and Lie algebra representations; (3) topology and differential geometry.The following are noteworthy features of this book: the style of exposition is a fusion of those common in the standard physics and mathematics literatures; the level of exposition varies from quite elementary to moderately advanced, so that the book is of interest to a wide audience; despite the diversity of the topics covered, there is a strong degree of thematic unity; much care is devoted to detailed cross-referencing so that, from any part of the book, the reader can trace easily where specific concepts or techniques are introduced.

Classical Mechanics With Mathematica

Author: Antonio Romano
Publisher: Springer Science & Business Media
ISBN: 0817683526
Size: 74.33 MB
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This textbook takes a broad yet thorough approach to mechanics, aimed at bridging the gap between classical analytic and modern differential geometric approaches to the subject.​ Developed by the author from 35 years of teaching experience, the presentation is designed to give students an overview of the many different models used through the history of the field—from Newton to Lagrange—while also painting a clear picture of the most modern developments. Throughout, it makes heavy use of the powerful tools offered by Mathematica​. The volume is organized into two parts. The first focuses on developing the mathematical framework of linear algebra and differential geometry necessary for the remainder of the book. Topics covered include tensor algebra, Euclidean and symplectic vector spaces, differential manifolds, and absolute differential calculus. The second part of the book applies these topics to kinematics, rigid body dynamics, Lagrangian and Hamiltonian dynamics, Hamilton–Jacobi theory, completely integrable systems, statistical mechanics of equilibrium, and impulsive dynamics, among others. Unique in its scope of coverage and method of approach, Classical Mechanics will be a very useful resource for graduate students and advanced undergraduates in applied mathematics and physics who hope to gain a deeper understanding of mechanics.

Introduction To Statistical Physics

Author: João Paulo Casquilho
Publisher: Cambridge University Press
ISBN: 1316213994
Size: 46.47 MB
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Rigorous and comprehensive, this textbook introduces undergraduate students to simulation methods in statistical physics. The book covers a number of topics, including the thermodynamics of magnetic and electric systems; the quantum-mechanical basis of magnetism; ferrimagnetism, antiferromagnetism, spin waves and magnons; liquid crystals as a non-ideal system of technological relevance; and diffusion in an external potential. It also covers hot topics such as cosmic microwave background, magnetic cooling and Bose–Einstein condensation. The book provides an elementary introduction to simulation methods through algorithms in pseudocode for random walks, the 2D Ising model, and a model liquid crystal. Any formalism is kept simple and derivations are worked out in detail to ensure the material is accessible to students from subjects other than physics.

Probability And Statistical Physics In St Petersburg

Author: V. Sidoravicius
Publisher: American Mathematical Soc.
ISBN: 1470422484
Size: 20.54 MB
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This book brings a reader to the cutting edge of several important directions of the contemporary probability theory, which in many cases are strongly motivated by problems in statistical physics. The authors of these articles are leading experts in the field and the reader will get an exceptional panorama of the field from the point of view of scientists who played, and continue to play, a pivotal role in the development of the new methods and ideas, interlinking it with geometry, complex analysis, conformal field theory, etc., making modern probability one of the most vibrant areas in mathematics.

Integrable Quantum Field Theories And Their Application

Author: Changrim Ahn
Publisher: World Scientific
ISBN: 9810247370
Size: 46.60 MB
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This volume includes several lecture notes on the fundamentals and elementary techniques of integrable field theories and on their applications to low-dimensional physics systems contributed by leading scientists in the respective fields. The main topics covered are various aspects of the thermodynamic Bethe ansatz, form factors, Calogero (and related) models, sigma models, conformal boundary conditions, etc. The volume presents both pedagogical material and a current research trend in the field.The proceedings have been selected for coverage in: ? Index to Scientific & Technical Proceedings (ISTP CDROM version / ISI Proceedings)