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This book provides a comprehensive introduction to equilibrium and non-equilibrium Green's function methods in many-body physics. It begins with a derivation of second quantisation for relativistic systems based on the many-body relativistic Dirac equation and its non-relativistic limit. The properties of equilibrium Green's functions are then described, with discussion of the two-time and Matsubara function methods. The coverage of non-equilibrium Green's function methods includes the diagrammatic techniques applicable to electrons and phonons using both the perturbation and variational approaches. Specific applications to steady-state and time-dependent quantum transport are presented in the final chapters. The book's accessible explanations, detailed derivations, and systematic treatment of the underlying theory make it a valuable resource for graduate students and early-career researchers. More than 200 problems have been included to support learning, with selected solutions available at the end of each chapter. Instructors benefit from access to the full solutions manual.
Spontaneous symmetry breaking lies at the heart of modern physics, shaping our understanding of matter, forces, and even the universe itself. From condensed matter physics to particle physics and cosmology, spontaneous symmetry breaking unifies phenomena that at first seem worlds apart. This graduate-level text offers a comprehensive yet accessible guide to the conceptual theory and practical consequences of spontaneous symmetry breaking. It introduces topics ranging from Noether's theorem, thermodynamic limits, and gauge freedoms to Nambu–Goldstone modes, topological defects, effective field theory, the Mermin–Wagner–Hohenberg–Coleman theorem, and the Anderson–Higgs mechanism within the Standard Model. Packed with exercises, with solutions available online, in-depth projects, and a myth-busting FAQ section addressing common pitfalls, this book equips readers to master both the fundamentals and modern frontiers of spontaneous symmetry breaking, making it an indispensable resource for students, teachers, and researchers.
Driven by advances in data science and machine learning, photonics has evolved rapidly in recent years and has transformed into a highly interdisciplinary field, connecting fundamental research with cutting-edge applications. Inspired by recent Nobel Prizes in Physics in 2021 and 2024, Conti highlights the interplay between photonics and spin glasses, a key concept for understanding the link between photon propagation and complex systems. Beginning with a study of black-body radiation, the book then revisits laser theory using techniques from non-equilibrium statistical mechanics. Through a step-by-step exploration of important photonic experiments, it bridges foundational concepts and advances in optical computing, with a focus on developing efficient hardware for classical and quantum artificial intelligence. This reveals the profound ties between complexity, photonics, and the future of AI technologies. The book will be a valuable resource for advanced undergraduate and graduate students and more practised researchers.
'Quantum Engineering' covers the theory, design, fabrication and applications of quantum coherent solid-state structures. This updated and expanded second edition provides a self-contained presentation of the theoretical methods and experimental results in both first and second waves of quantum technology innovation. Topics span the quantum theory of electric circuits, theoretical methods of quantum optics in application to solid-state circuits, the quantum theory of noise, decoherence and measurements, Landauer formalism for quantum transport, the physics of weak superconductivity and the physics of two-dimensional electron gas in semiconductor heterostructures. The author introduces microscopic ion- and defect-based qubits, currently among the most successful platforms for quantum computation and quantum sensing. Reflecting the significant progress of quantum hardware, state-of-the-art implementations such as quantum metamaterials and quantum reservoir computing are also added to the discussion. Written for graduate students in physics, this book also serves electronic engineers working in quantum engineering.
The study of magnetism has driven progress in experimental science for centuries, and demonstrates how ground-breaking theoretical advances can be translated directly into essential, transformative technology. Now in an expanded second edition, this popular textbook provides comprehensive coverage of the theory and practical applications of magnetism and magnetic materials. The text has been updated throughout to address significant developments from the last decade, including new theoretical insights, advanced experimental probes, and thin film technology. A new chapter covers the important topic of transverse magnetotransport and effects of topology. The book is extensively illustrated with over 700 figures conveying important experimental data, concepts and applications, and each self-contained chapter concludes with a summary section, a list of further reading and a set of exercises. The text contains a wealth of useful information that will be of interest to graduate students and researchers in physics, materials science and engineering.
Computational mineralogy is fast becoming the most effective and quantitatively accurate method for successfully determining structures, properties and processes at the extreme pressure and temperature conditions that exist within the Earth's deep interior. It is now possible to simulate complex mineral phases using a variety of theoretical computational techniques that probe the microscopic nature of matter at both the atomic and sub-atomic levels. This introductory guide is for geoscientists as well as researchers performing measurements and experiments in a lab, those seeking to identify minerals remotely or in the field, and those seeking specific numerical values of particular physical properties. Written in a user- and property-oriented way, and illustrated with calculation examples for different mineral properties, it explains how property values are produced, how to tell if they are meaningful or not, and how they can be used alongside experimental results to unlock the secrets of the Earth.
As physical science advances, theoretical simulations become increasingly reflective of realistic systems, and experimental observations become more precise and refined. Thus, going beyond the Born–Oppenheimer approximation is inevitable. This book bases its discussion of condensed matter physics on the Schrödinger equation, considering both nuclear and electronic degrees of freedom. Particular attention is given to two types of phenomena: those, such as nuclear quantum effects, for which the Born–Oppenheimer approximation, although applicable in principle, is progressively weakened in practice, and those that cannot be applied at all, such as phenomena exhibiting non-adiabatic effects. In practical systems, the full quantum nature of condensed matter, as emphasized in this book, cannot be overlooked when performing accurate simulations or measurements of material properties. This book offers state-of-the-art quantum theoretical and experimental methods, valuable for undergraduates, graduates, researchers, and industry professionals in fields such as physics, chemistry, materials science, energy, and environmental science.
Quantum many-body systems are a central feature of condensed matter physics, relevant to important, modern research areas such as ultrafast light-matter interactions and quantum information. This book offers detailed coverage of the contour Green's function formalism – an approach that can be successfully applied to solve the quantum many-body and time-dependent problems present within such systems. Divided into three parts, the text provides a structured overview of the relevant theoretical and practical tools, with specific focus on the Schwinger-Keldysh formalism. Part I introduces the mathematical frameworks that make use of Green's functions in normal phase states. Part II covers fermionic superfluid phases with discussion of topics such as the BCS-BEC crossover and superconducting systems. Part III deals with the application of the Schwinger-Keldysh formalism to various topics of experimental interest. Graduate students and researchers will benefit from the book's comprehensive treatment of the subject matter and its novel arrangement of topics.
Artificial intelligence is transforming industries and society, but its high energy demands challenge global sustainability goals. Biological intelligence, in contrast, offers both good performance and exceptional energy efficiency. Neuromorphic computing, a growing field inspired by the structure and function of the brain, aims to create energy-efficient algorithms and hardware by integrating insights from biology, physics, computer science, and electrical engineering. This concise and accessible book delves into the principles, mechanisms, and properties of neuromorphic systems. It opens with a primer on biological intelligence, describing learning mechanisms in both simple and complex organisms, then turns to the application of these principles and mechanisms in the development of artificial synapses and neurons, circuits, and architectures. The text also delves into neuromorphic algorithm design, and the unique challenges faced by algorithmic researchers working in this area. The book concludes with a selection of practice problems, with solutions available to instructors online.
Extreme fluctuations in oil prices (such as the dramatic fall from mid-2014 into 2015) raise important strategic questions for both importers and exporters. In this volume, specialists from the US, the Middle East, Europe and Asia examine the rapidly evolving dynamic in the energy landscape, including renewable and nuclear power, challenges to producers including the shale revolution, and legal issues. Each chapter provides in-depth analysis and clear policy recommendations.
Stochastic thermodynamics has emerged as a comprehensive theoretical framework for a large class of non-equilibrium systems including molecular motors, biochemical reaction networks, colloidal particles in time-dependent laser traps, and bio-polymers under external forces. This book introduces the topic in a systematic way, beginning with a dynamical perspective on equilibrium statistical physics. Key concepts like the identification of work, heat and entropy production along individual stochastic trajectories are then developed and shown to obey various fluctuation relations beyond the well-established linear response regime. Representative applications are then discussed, including simple models of molecular motors, small chemical reaction networks, active particles, stochastic heat engines and information machines involving Maxwell demons. This book is ideal for graduate students and researchers of physics, biophysics, and physical chemistry, with an interest in non-equilibrium phenomena.
This accessible text is an introduction to the theory of phase transitions and its application to real materials. Assuming some familiarity with thermodynamics and statistical mechanics, the book begins with a primer on the thermodynamics of equilibrium phase transitions, including the mean-field and Ginzburg-Landau approaches. The general kinetic features and dynamics of phase transitions are explained, ensuring that readers are familiar with the key physical concepts. With the foundations established, the general theory is applied to the study of phase transitions in a wide range of materials including ferroic materials, caloric materials, liquid crystals and glasses. Non-equilibrium phase transitions, superconductors and quantum phase transitions are also covered. Including exercises throughout and solutions available online, this text is suitable for graduate courses as well as researchers in physics and materials science seeking a primer on popular and emerging research topics.
This book explores the fractionalization of particles in physics, how interactions between individual particles and with their background can modify their fundamental quantum states. Covering a large breadth of topics with an example-driven approach, this comprehensive text explains why phases of matter must be described in terms of both symmetries and their topology. The majority of important results are derived in full with explanations provided, while exercises at the end of each section allow readers to extend and develop their understanding of key topics. The first part presents polyacetylene as the paradigmatic material in which electric charge can be fractionalized, while the second part introduces the notion of invertible topological phases of matter. The final part is devoted to the 'ten-fold way', a classification of topological insulators or superconductors. The text requires a solid understanding of quantum mechanics and is a valuable resource for graduate students and researchers in physics.
The Green's function method is among the most powerful and versatile formalisms in physics, and its nonequilibrium version has proved invaluable in many research fields. With entirely new chapters and updated example problems, the second edition of this popular text continues to provide an ideal introduction to nonequilibrium many-body quantum systems and ultrafast phenomena in modern science. Retaining the unique and self-contained style of the original, this new edition has been thoroughly revised to address interacting systems of fermions and bosons, simplified many-body approaches like the GKBA, the Bloch equations and the Boltzmann equations and the connection between Green's functions and newly developed time-resolved spectroscopy techniques. Small gaps in the theory have been filled, and frequently overlooked subtleties have been systematically highlighted and clarified. With an abundance of illustrative examples, insightful discussions and modern applications, this book remains the definitive guide for students and researchers alike.
This book deals with the discovery and explanation of the quantum Hall effect and its fundamental principles. It is meant for undergraduate and graduate students of physics, engineering, and applied sciences studying condensed matter physics. Doctoral students and researchers of this subject will also find it equally useful. It begins with a historical overview of this effect wherein the experiment and the physical systems are described. It progresses to cover discrete symmetries like inversion symmetry, time reversal symmetry, particle-hole symmetry, and chiral symmetry. It also examines how the Hamiltonian transforms under such symmetry operations. Two 1D models, namely the Su-Schrieffer-Heeger (SSH) model and a Kitaev chain with superconducting correlations, are discussed too. Then, the quantum Hall effect in graphene is explained. Further, the spin Hall effect is studied which may have prospects of using graphene as spintronic devices. The book ends with a brief review on fractional quantum Hall effect.
Renormalization group theory of tensor network states provides a powerful tool for studying quantum many-body problems and a new paradigm for understanding entangled structures of complex systems. In recent decades the theory has rapidly evolved into a universal framework and language employed by researchers in fields ranging from condensed matter theory to machine learning. This book presents a pedagogical and comprehensive introduction to this field for the first time. After an introductory survey on the major advances in tensor network algorithms and their applications, it introduces step-by-step the tensor network representations of quantum states and the tensor-network renormalization group methods developed over the past three decades. Basic statistical and condensed matter physics models are used to demonstrate how the tensor network renormalization works. An accessible primer for scientists and engineers, this book would also be ideal as a reference text for a graduate course in this area.
Many materials can be modeled either as discrete systems or as continua, depending on the scale. At intermediate scales it is necessary to understand the transition from discrete to continuous models and variational methods have proved successful in this task, especially for systems, both stochastic and deterministic, that depend on lattice energies. This is the first systematic and unified presentation of research in the area over the last 20 years. The authors begin with a very general and flexible compactness and representation result, complemented by a thorough exploration of problems for ferromagnetic energies with applications ranging from optimal design to quasicrystals and percolation. This leads to a treatment of frustrated systems, and infinite-dimensional systems with diffuse interfaces. Each topic is presented with examples, proofs and applications. Written by leading experts, it is suitable as a graduate course text as well as being an invaluable reference for researchers.
Turbulence plays a crucial role in contexts ranging from galaxy formation to heavy atomic nuclei, from jet engines to arterial blood flow, challenging engineers, physicists, and mathematicians. Recently, turbulence of quantum fluids displaying superfluidity has emerged as an exciting area of interdisciplinary research that spans fluid dynamics, low-temperature physics, and Bose-Einstein condensation. The first book on quantum turbulence, this work describes state-of-the-art results and techniques, stressing analogies and differences with classical turbulence. The authors focus in particular on low temperature phases of liquid helium, drawing on evidence from recent experiments, theory, and numerical simulations. Written by leading figures in the field, this is a go-to reference for students and researchers at all levels.