Abstract Nonlinear physics has grown from a collection of exotic examples of nonstandard behavior to an all-embracing scientific methodology. Many examples come from condensed matter physics. This book presents a unified view of many-body condensed matter systems as essentially nonlinear structures capable of exhibiting such features as chaos, coherence, solution formation and phase transitions. The book provides an overview of nonlinear phenomena in science, introduces phase transitions and criticality, and includes a comprehensive exposition of methods and results in the analysis of nonlinear differential equations. To equip the reader with concrete skills in tackling nonlinear problems in physics, the authors also analyze important applications such as metamagnetism, superconductivity, the Hubbard Hamiltonian and the multielectron atom. The book can serve as both a compendium of facts and references related to nonlinear condensed matter physics and a practical introduction to current research methods and the field in general.
Abstract Nonlinear physics has grown from a collection of exotic examples of nonstandard behavior to an all-embracing scientific methodology. Many examples come from condensed matter physics. This book presents a unified view of many-body condensed matter systems as essentially nonlinear structures capable of exhibiting such features as chaos, coherence, solution formation and phase transitions. The book provides an overview of nonlinear phenomena in science, introduces phase transitions and criticality, and includes a comprehensive exposition of methods and results in the analysis of nonlinear differential equations. To equip the reader with concrete skills in tackling nonlinear problems in physics, the authors also analyze important applications such as metamagnetism, superconductivity, the Hubbard Hamiltonian and the multielectron atom. The book can serve as both a compendium of facts and references related to nonlinear condensed matter physics and a practical introduction to current research methods and the field in general.
Modern experimental developments in condensed matter and ultracold atom physics present formidable challenges to theorists. This book provides a pedagogical introduction to quantum field theory in many-particle physics, emphasizing the applicability of the formalism to concrete problems. This second edition contains two new chapters developing path integral approaches to classical and quantum nonequilibrium phenomena. Other chapters cover a range of topics, from the introduction of many-body techniques and functional integration, to renormalization group methods, the theory of response functions, and topology. Conceptual aspects and formal methodology are emphasized, but the discussion focuses on practical experimental applications drawn largely from condensed matter physics and neighboring fields. Extended and challenging problems with fully worked solutions provide a bridge between formal manipulations and research-oriented thinking. Aimed at elevating graduate students to a level where they can engage in independent research, this book complements graduate level courses on many-particle theory.
Critical phenomena is one of the most exciting areas of modern physics. This 2007 book provides a thorough but economic introduction into the principles and techniques of the theory of critical phenomena and the renormalization group, from the perspective of modern condensed matter physics. Assuming basic knowledge of quantum and statistical mechanics, the book discusses phase transitions in magnets, superfluids, superconductors, and gauge field theories. Particular attention is given to topics such as gauge field fluctuations in superconductors, the Kosterlitz-Thouless transition, duality transformations, and quantum phase transitions - all of which are at the forefront of physics research. This book contains numerous problems of varying degrees of difficulty, with solutions. These problems provide readers with a wealth of material to test their understanding of the subject. It is ideal for graduate students and more experienced researchers in the fields of condensed matter physics, statistical physics, and many-body physics.
Abstract Phase transitions and critical phenomena have consistently been among the principal subjects of active studies in statistical physics. The simple act of transforming one state of matter or phase into another, for instance by changing the temperature, has always captivated the curious mind. This book provides an introductory account on the theory of phase transitions and critical phenomena, a subject now recognized to be indispensable for students and researchers from many fields of physics and related disciplines. The first five chapters are very basic and quintessential, and cover standard topics such as mean-field theories, the renormalization group and scaling, universality, and statistical field theory methods. The remaining chapters develop more advanced concepts, including conformal field theory, the Kosterlitz-Thouless transition, the effects of randomness, percolation, exactly solvable models, series expansions, duality transformations, and numerical techniques. Moreover, a comprehensive series of appendices expand and clarify several issues not developed in the main text. The important role played by symmetry and topology in understanding the competition between phases and the resulting emergent collective behaviour, giving rise to rigidity and soft elementary excitations, is stressed throughout the book. Serious attempts have been directed toward a self-contained modular approach so that the reader does not have to refer to other sources for supplementary information. Accordingly, most of the concepts and calculations are described in detail, sometimes with additional/auxiliary descriptions given in appendices and exercises. The latter are presented as the topics develop with solutions found at the end of the book, thus giving the text a self-learning character.
This innovative and modular textbook combines classical topics in thermodynamics, statistical mechanics and many-body theory with the latest developments in condensed matter physics research. Written by internationally renowned experts and logically structured to cater for undergraduate and postgraduate students and researchers, it covers the underlying theoretical principles and includes numerous problems and worked examples to put this knowledge into practice. Three main streams provide a framework for the book; beginning with thermodynamics and classical statistical mechanics, including mean field approximation, fluctuations and the renormalization group approach to critical phenomena. The authors then examine quantum statistical mechanics, covering key topics such as normal Fermi and Luttinger liquids, superfluidity and superconductivity. Finally, they explore classical and quantum kinetics, Anderson localization and quantum interference, and disordered Fermi liquids. Unique in providing a bridge between thermodynamics and advanced topics in condensed matter, this textbook is an invaluable resource to all students of physics.
The methods of quantum field theory underpin many conceptual advances in contemporary condensed matter physics and neighbouring fields. This book provides a praxis-oriented and pedagogical introduction to quantum field theory in many-particle physics, emphasizing the application of theory to real physical systems. This third edition is organized into two parts: the first half of the text presents a streamlined introduction, elevating readers to a level where they can engage with contemporary research literature, from the introduction of many-body techniques and functional integration to renormalization group methods, and the second half addresses a range of advanced topics including modern aspects of gauge theory, topological and relativistic quantum matter, and condensed matter physics out of thermal equilibrium. At all stages, the text seeks a balance between methodological aspects of quantum field theory and practical applications. Extended problems with worked solutions provide a bridge between formal theory and a research-oriented approach.
Quantum Many-Body Physics: A Path Integral Approach offers a fresh perspective on quantum phenomena in condensed matter physics. This comprehensive book provides a powerful and versatile framework for understanding complex problems in systems such as ultracold atoms, superfluids, and superconductors. The text begins with a solid foundation in canonical quantum field theory before progressing to advanced topics, ensuring readers develop both deep conceptual understanding and practical skills. Features include: Concise yet thorough coverage of path integral methods Practical applications to real-world quantum systems Problem-solving techniques that bridge theory and experiment Designed for graduate students in physics and related disciplines, this book serves as an essential resource for those aiming to advance their studies in quantum mechanics. Researchers in condensed matter physics, quantum optics, and quantum information will also find valuable insights to support their work on the next breakthroughs in the field.