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Introduction To The Statistical Physics Of Integrable Many Body Systems

Author: Ladislav Šamaj
Publisher: Cambridge University Press
ISBN: 1107067669
Size: 43.24 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.

Order Disorder And Criticality

Author: Yurij Holovatch
Publisher: World Scientific
ISBN: 9814632694
Size: 75.10 MB
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This book is the fourth in the series of review papers on advanced problems of phase transitions and critical phenomena, the first three volumes appeared in 2004, 2007, and 2012. It presents reviews in those aspects of criticality and related subjects that have currently attracted much attention due to new and essential contributions. The contents are divided into five chapters, and they include: anomalous diffusion, kinetics of pattern formation, scaling, renormalization group approaches in soft matter and socio-physics, Monte Carlo simulation of critical Casimir forces. As with the first three volumes, this book is based on the review lectures that were given in Lviv (Ukraine) at the “Ising lectures” — a traditional annual workshop on phase transitions and critical phenomena which aims to bring together scientists working in these fields with university students and those who are interested in the subject. Contents:Scaling and Finite-Size Scaling above the Upper Critical Dimension (R Kenna and B Berche)Monte Carlo Simulation of Critical Casimir Forces (O A Vasilyev)Non-ergodicity and Ageing in Anomalous Diffusion (R Metzler)Kinetics of Pattern Formation: Mesoscopic and Atomistic Modelling (H Zapolsky)A Renormalization Group Like Model for a Democratic Dictatorship (S Galam) Readership: Researchers, advanced undergraduates and graduate students in physics; non-expert scientists interested in phase transitions and critical phenomena. Keywords:Phase Transitions;Criticality;Scaling;Complex Systems

Back Of The Envelope Quantum Mechanics

Author: Maxim Olshanii
Publisher: World Scientific
ISBN: 9814508489
Size: 66.23 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: 40.37 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.

Quantum Many Body Systems In One Dimension

Author: Zachary N C Ha
Publisher: World Scientific
ISBN: 9814500372
Size: 75.82 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

Brownian Ratchets

Author: David Cubero
Publisher: Cambridge University Press
ISBN: 1316538907
Size: 50.47 MB
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Illustrating the development of Brownian ratchets, from their foundations, to their role in the description of life at the molecular scale and in the design of artificial nano-machinery, this text will appeal to both advanced graduates and researchers entering the field. Providing a self-contained introduction to Brownian ratchets, devices which rectify microscopic fluctuations, Part I avoids technicalities and sets out the broad range of physical systems where the concept of ratchets is relevant. Part II supplies a single source for a complete and modern theoretical analysis of ratchets in regimes such as classical vs quantum and stochastic vs deterministic, and in Part III readers are guided through experimental developments in different physical systems, each highlighting a specific unique feature of ratchets. The thorough and systematic approach to the topic ensures that this book provides a complete guide to Brownian ratchets for newcomers and established researchers in physics, biology and biochemistry.

New Developments Of Integrable Systems And Long Ranged Interaction Models

Author: Ge Mo-lin
Publisher: World Scientific
ISBN: 9814549754
Size: 42.81 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.

Introduction To Nonextensive Statistical Mechanics

Author: Constantino Tsallis
Publisher: Springer Science & Business Media
ISBN: 0387853588
Size: 26.70 MB
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Metaphors, generalizations and unifications are natural and desirable ingredients of the evolution of scientific theories and concepts. Physics, in particular, obviously walks along these paths since its very beginning. This book focuses on nonextensive statistical mechanics, a current generalization of Boltzmann-Gibbs (BG) statistical mechanics, one of the greatest monuments of contemporary physics. Conceived more than 130 years ago by Maxwell, Boltzmann and Gibbs, the BG theory exhibits uncountable – some of them impressive – successes in physics, chemistry, mathematics, and computational sciences, to name a few. Presently, more than two thousand publications, by over 1800 scientists around the world, have been dedicated to the nonextensive generalization. Remarkable applications have emerged, and its mathematical grounding is by now relatively well established. A pedagogical introduction to its concepts – nonlinear dynamics, extensivity of the nonadditive entropy, global correlations, generalization of the standard CLT’s, among others – is presented in this book as well as a selection of paradigmatic applications in various sciences together with diversified experimental verifications of some of its predictions. This is the first pedagogical book on the subject, written by the proponent of the theory Presents many applications to interdisciplinary complex phenomena in virtually all sciences, ranging from physics to medicine, from economics to biology, through signal and image processing and others Offers a detailed derivation of results, illustrations and for the first time detailed presentation of Nonextensive Statistical Mechanics

Classical Mechanics With Mathematica

Author: Antonio Romano
Publisher: Springer Science & Business Media
ISBN: 0817683526
Size: 30.80 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.

Nuclear Particle And Many Body Physics

Author: Philip Morse
Publisher: Elsevier
ISBN: 0323143032
Size: 78.40 MB
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Nuclear, Particle, and Many Body Physics, Volume I is a collection of scientific papers dedicated to the memory of Amos de-Shalit, a distinguished physicist. The book contains chapters that discuss various studies in the field of nuclear and particle physics. The text covers such topics as chemical binding in classical Coulomb lattices; algebraic treatment of subsidiary conditions in dual resonance models; the complete Schwarzschild solution; the investigation of nucleon-nucleon correlations by means of high-energy scattering; and some aspects on the magnetic-dipole moments of states in near-spherical nuclei. Theoretical, experimental, and nuclear physicists, researchers, and students in the field of physics will find the book invaluable.