This book is a self-contained advanced textbook on the mathematical-physical aspects of quantum many-body systems, which begins with a pedagogical presentation of the necessary background information before moving on to subjects of active research, including topological phases of matter. The book explores in detail selected topics in quantum spin systems and lattice electron systems, namely, long-range order and spontaneous symmetry breaking in the antiferromagnetic Heisenberg model in two or higher dimensions (Part I), Haldane phenomena in antiferromagnetic quantum spin chains and related topics in topological phases of quantum matter (Part II), and the origin of magnetism in various versions of the Hubbard model (Part III). Each of these topics represents certain nontrivial phenomena or features that are invariably encountered in a variety of quantum many-body systems, including quantum field theory, condensed matter systems, cold atoms, and artificial quantum systems designed for future quantum computers. The book's main focus is on universal properties of quantum many-body systems. The book includes roughly 50 problems with detailed solutions. The reader only requires elementary linear algebra and calculus to comprehend the material and work through the problems. Given its scope and format, the book is suitable both for self-study and as a textbook for graduate or advanced undergraduate classes.

This textbook presents a concise yet detailed introduction to quantum physics. Concise, because it condenses the essentials to a few principles. Detailed, because these few principles - necessarily rather abstract - are illustrated by several telling examples. A fairly complete overview of the conventional quantum mechanics curriculum is the primary focus, but the huge field of statistical thermodynamics is covered as well. The text explains why a few key discoveries shattered the prevailing broadly accepted classical view of physics. First, matter appears to consist of particles which, when propagating, resemble waves. Consequently, some observable properties cannot be measured simultaneously with arbitrary precision. Second, events with single particles are not determined, but are more or less probable. The essence of this is that the observable properties of a physical system are to be represented by non-commuting mathematical objects instead of real numbers. Chapters on exceptionally simple, but highly instructive examples illustrate this abstract formulation of quantum physics. The simplest atoms, ions, and molecules are explained, describing their interaction with electromagnetic radiation as well as the scattering of particles. A short introduction to many particle physics with an outlook on quantum fields follows. There is a chapter on maximally mixed states of very large systems, that is statistical thermodynamics. The following chapter on the linear response to perturbations provides a link to the material equations of continuum physics. Mathematical details which would hinder the flow of the main text have been deferred to an appendix. The book addresses university students of physics and related fields. It will attract graduate students and professionals in particular who wish to systematize or refresh their knowledge of quantum physics when studying specialized texts on solid state and materials physics, advanced optics, and other modern fields.

This book explains theoretical and technological aspects of amorphous drug formulations. It is intended for all those wishing to increase their knowledge in the field of amorphous pharmaceuticals. Conversion of crystalline material into the amorphous state, as described in this book, is a way to overcome limited water solubility of drug formulations, in this way enhancing the chemical activity and bioavailability inside the body. Written by experts from various fields and backgrounds, the book introduces to fundamental physical aspects (explaining differences between the ordered and the disordered solid states, the enhancement of solubility resulting from drugs amorphization, physical instability and how it can be overcome) as well as preparation and formulation procedures to produce and stabilize amorphous pharmaceuticals. Readers will thus gain a well-funded understanding and find a multi-faceted discussion of the properties and advantages of amorphous drugs and of the challenges in producing and stabilizing them. The book is an ideal source of information for researchers and students as well as professionals engaged in research and development of amorphous pharmaceutical products.

This third edition of Statistical Physics of Complex Systems has been expanded to provide more examples of applications of concepts and methods from statistical physics to the modeling of complex systems. These include avalanche dynamics in materials, models of social agents like road traffic or wealth repartition, the real space aspects of biological evolution dynamics, propagation phenomena on complex networks, formal neural networks and their connection to constraint satisfaction problems. This course-tested textbook provides graduate students and non-specialists with a basic understanding of the concepts and methods of statistical physics and demonstrates their wide range of applications to interdisciplinary topics in the field of complex system sciences, including selected aspects of theoretical modeling in biology and the social sciences. It covers topics such as non-conserved particles, evolutionary population dynamics, networks, properties of both individual and coupled simple dynamical systems, and convergence theorems, as well as short appendices that offer helpful hints on how to perform simple stochastic simulations in practice. The original spirit of the book is to remain accessible to a broad, non-specialized readership. The format is a set of concise, modular, and self-contained topical chapters, avoiding technicalities and jargon as much as possible, and complemented by a wealth of worked-out examples, so as to make this work useful as a self-study text or as textbook for short courses.

This book discusses the elementary ideas and tools needed for open quantum systems in a comprehensive manner. The emphasis is given to both the traditional master equation as well as the functional (path) integral approaches. It discusses the basic paradigm of open systems, the harmonic oscillator and the two-level system in detail. The traditional topics of dissipation and tunneling, as well as the modern field of quantum information, find a prominent place in the book. Assuming a basic background of quantum and statistical mechanics, this book will help readers familiarize with the basic tools of open quantum systems. Open quantum systems is the study of quantum dynamics of the system of interest, taking into account the effects of the ambient environment. It is ubiquitous in the sense that any system could be envisaged to be surrounded by its environment which could naturally exert its influence on it. Open quantum systems allows for a systematic understanding of irreversible processes such as decoherence and dissipation, of the essence in order to have a correct understanding of realistic quantum dynamics and also for possible implementations. This would be essential for a possible development of quantum technologies.

This book presents the Proceedings of the 54th Winter School of Theoretical Physics on Simplicity of Complexity in Economic and Social Systems, held in Ladek Zdroj, Poland, from 18 to 24 February 2018. The purpose of the book is to introduce the new interdisciplinary research that links statistical physics, and particular attention is given to link physics of complex systems, with financial analysis and sociology. The main tools used in these areas are numerical simulation of agents behavior and the interpretation of results with the help of complexity methods, therefore a background in statistical physics and in physics of phase transition is necessary to take the first steps towards these research fields called econophysics and sociophysics. In this perspective, the book is intended to graduated students and young researchers who want to begin the study of this established new area, which connects physicists, economists, sociologists and IT professionals, to better understand complexity phenomena existing not only in physics but also in complex systems being seemingly far from traditional view at physics.

Defrosting for Air Source Heat Pumps: Research, Analysis and Methods presents a detailed analysis of the methods, processes and problems relating to defrosting, a necessary requirement to maintain the performance of ASHP units. Readers will gain a deeper understanding of control strategies and system design optimization methods that improve the performance and reliability of units. The book discusses the most recent experimental and numerical studies of reverse cycle defrosting and the most widely used defrosting method for ASHP. Techno-economic considerations are also presented, as is the outlook for the future. This book is a valuable resource for research students and academics of thermal energy and mechanical engineering, especially those focusing on defrosting for ASHP, heating, ventilation and energy efficiency, as well as engineers and professionals engaged in the development and management of heat pump machinery.

This book focuses on a central question in the field of complex systems: Given a fluctuating (in time or space), uni- or multi-variant sequentially measured set of experimental data (even noisy data), how should one analyse non-parametrically the data, assess underlying trends, uncover characteristics of the fluctuations (including diffusion and jump contributions), and construct a stochastic evolution equation? Here, the term "non-parametrically" exemplifies that all the functions and parameters of the constructed stochastic evolution equation can be determined directly from the measured data. The book provides an overview of methods that have been developed for the analysis of fluctuating time series and of spatially disordered structures. Thanks to its feasibility and simplicity, it has been successfully applied to fluctuating time series and spatially disordered structures of complex systems studied in scientific fields such as physics, astrophysics, meteorology, earth science, engineering, finance, medicine and the neurosciences, and has led to a number of important results. The book also includes the numerical and analytical approaches to the analyses of complex time series that are most common in the physical and natural sciences. Further, it is self-contained and readily accessible to students, scientists, and researchers who are familiar with traditional methods of mathematics, such as ordinary, and partial differential equations. The codes for analysing continuous time series are available in an R package developed by the research group Turbulence, Wind energy and Stochastic (TWiSt) at the Carl von Ossietzky University of Oldenburg under the supervision of Prof. Dr. Joachim Peinke. This package makes it possible to extract the (stochastic) evolution equation underlying a set of data or measurements.

The model investigated in this work, a particular cellular automaton with stochastic evolution, was introduced as the simplest case of self-organized-criticality, that is, a dynamical system which shows algebraic long-range correlations without any tuning of parameters. The author derives exact results which are potentially also interesting outside the area of critical phenomena. Exact means also site-by-site and not only ensemble average or coarse graining. Very complex and amazingly beautiful periodic patterns are often generated by the dynamics involved, especially in deterministic protocols in which the sand is added at chosen sites. For example, the author studies the appearance of allometric structures, that is, patterns which grow in the same way in their whole body, and not only near their boundaries, as commonly occurs. The local conservation laws which govern the evolution of these patterns are also presented. This work has already attracted interest, not only in non-equilibrium statistical mechanics, but also in mathematics, both in probability and in combinatorics. There are also interesting connections with number theory. Lastly, it also poses new questions about an old subject. As such, it will be of interest to computer practitioners, demonstrating the simplicity with which charming patterns can be obtained, as well as to researchers working in many other areas.

Philosophy in Reality offers a new vision of the relation between science and philosophy in the framework of a non-propositional logic of real processes, grounded in the physics of the real world. This logical system is based on the work of the Franco-Romanian thinker Stephane Lupasco (1900-1988), previously presented by Joseph Brenner in the book Logic in Reality (Springer, 2008). The present book was inspired in part by the ancient Chinese Book of Changes (I Ching) and its scientific-philosophical discussion of change. The emphasis in Philosophy in Reality is on the recovery of dialectics and semantics from reductionist applications and their incorporation into a new synthetic paradigm for knowledge. Through an original re-interpretation of both classical and modern Western thought, this book addresses philosophical issues in scientific fields as well as long-standing conceptual problems such as the origin, nature and role of meaning, the unity of knowledge and the origin of morality. In a rigorous transdisciplinary manner, it discusses foundational and current issues in the physical sciences - mathematics, information, communication and systems theory and their implications for philosophy. The same framework is applied to problems of the origins of society, the transformation of reality by human subjects, and the emergence of a global, sustainable information society. In summary, Philosophy in Reality provides a wealth of new perspectives and references, supporting research by both philosophers and physical and social scientists concerned with the many facets of reality.

The Minority Game is a physicist's attempt to explain market behaviour by the interaction between traders. With a minimal set of ingredients and drastic assumptions, this model reproduces market ecology among different types of traders. Its emphasis is on speculative trading and information flow. The book first describes the philosophy lying behind the conception of the Minority Game in 1997, and includes in particular a discussion about the El Farol bar problem. It then reviews the main steps in later developments, including both the theory and its applications to market phenomena. 'Minority Games' gives a colourful and stylized, but also realistic picture of how financial markets operate.

This volume constitutes the proceedings of NetSci-X 2020: the Sixth International School and Conference on Network Science, which was held in Tokyo, Japan, in January 2020. NetSci-X is the Network Science Society's winter conference series that covers a wide variety of interdisciplinary topics on networks. Participants come from various fields, including (but not limited to): mathematics, physics, computer science, social sciences, management and marketing sciences, organization science, communication science, systems science, biology, ecology, neuroscience, medicine, as well as business. This volume consists of contributed papers that have been accepted to NetSc-X 2020 through a rigorous peer review process. Researchers, students, and professionals will gain first-hand information about today's cutting-edge research frontier of network science.

Measurements, Mechanisms, and Models of Heat Transport offers an interdisciplinary approach to the dynamic response of matter to energy input. Using a combination of fundamental principles of physics, recent developments in measuring time-dependent heat conduction, and analytical mathematics, this timely reference summarizes the relative advantages of currently used methods, and remediates flaws in modern models and their historical precursors. Geophysicists, physical chemists, and engineers will find the book to be a valuable resource for its discussions of radiative transfer models and the kinetic theory of gas, amended to account for atomic collisions being inelastic. This book is a prelude to a companion volume on the thermal state, formation, and evolution of planets. Covering both microscopic and mesoscopic phenomena of heat transport, Measurements, Mechanisms, and Models of Heat Transport offers both the fundamental knowledge and up-to-date measurements and models to encourage further improvem

Nonextensive statistical mechanics is now a rapidly growing field and a new stream in the research of the foundations of statistical mechanics. This generalization of the well-known Boltzmann--Gibbs theory enables the study of systems with long-range interactions, long-term memories or multi-fractal structures. This book consists of a set of self-contained lectures and includes additional contributions where some of the latest developments -- ranging from astro- to biophysics -- are covered. Addressing primarily graduate students and lecturers, this book will also be a useful reference for all researchers working in the field.

This book offers a didactic and a self-contained treatment of the physics of liquid and flowing matter with a statistical mechanics approach. Experimental and theoretical methods that were developed to study fluids are now frequently applied to a number of more complex systems generically referred to as soft matter. As for simple liquids, also for complex fluids it is important to understand how their macroscopic behavior is determined by the interactions between the component units. Moreover, in recent years new and relevant insights have emerged from the study of anomalous phases and metastable states of matter. In addition to the traditional topics concerning fluids in normal conditions, the authors of this book discuss recent developments in the field of disordered systems in condensed and soft matter. In particular they emphasize computer simulation techniques that are used in the study of soft matter and the theories and study of slow glassy dynamics. For these reasons the book includes a specific chapter about metastability, supercooled liquids and glass transition. The book is written for graduate students and active researchers in the field.

This book focuses on the characteristics of optical radiation, or a spectrum, emitted by various plasmas. In plasma, the same atomic species can produce quite different spectra, or colors depending on the nature of the plasma. This book gives a theoretical framework, by which a particular spectrum can be interpreted correctly and coherently. The uniqueness of the book lies in its comprehensive treatment of the intensity distribution of spectral lines and the population density distribution among the atomic levels, in plasma. It is intended to provide beginners with a good perspective of the field, laying out the physics in an extremely clear manner, starting from an elementary level. A very useful feature of the book is the asterisked sections and chapters which can be skipped by readers, who only wish to gain a quick and basic introduction to plasma spectroscopy. It will also be very useful to researchers working actively in the field, acting as a guide for carrying out experiments and interpreting experimental observations.

This book continues the process of systematization of knowledge about convection. It is important to put the current knowledge on weakly and strongly stratified convection in order, and provide a comprehensive description of the marginal, weakly nonlinear and fully developed stages of convective flow in both cases. The book provides a short compendium of knowledge on the linear and weakly nonlinear limits of the Boussinesq convection, and a review of the theory on fully developed Boussinesq convection. The third chapter is devoted to a detailed derivation and a study of the three aforementioned stages of stratified (anelastic) convection, with a full solution in the marginal stage provided for the first time. Detailed and systematic explanations are given. The book is intended mainly as a textbook for courses on hydrodynamics and convective flows, for the use of lecturers and students; however, it also serves for the entire scientific community as a practical reference.

This book is unique in occupying a gap between standard undergraduate texts and more advanced texts on quantum field theory. It covers a range of renormalization methods with a clear physical interpretation (and motivation), including meanfield theories and high-temperature and low-density
expansions. It then proceeds by easy steps to the famous epsilon-expansion, ending up with the first-order corrections to critical exponents beyond mean-field theory. Nowadays, there is widespread interest in applications of renormalization methods to various topics ranging over soft condensed
matter, engineering dynamics, traffic queueing and fluctuations in the stock market. Hence macroscopic systems are also included, with particular emphasis on the archetypal problem of fluid turbulence. The book is also unique in making this material accessible to readers other than theoretical
physicists, as it requires only the basic physics and mathematics which should be known to most scientists, engineers and mathematicians.

Though the reductionist approachto biology and medicine has led to several imp- tant advances, further progresses with respect to the remaining challenges require integration of representation, characterization and modeling of the studied systems along a wide range of spatial and time scales. Such an approach, intrinsically - lated to systems biology, is poised to ultimately turning biology into a more precise and synthetic discipline, paving the way to extensive preventive and regenerative medicine [1], drug discovery [20] and treatment optimization [24]. A particularly appealing and effective approach to addressing the complexity of interactions inherent to the biological systems is provided by the new area of c- plex networks [34, 30, 8, 13, 12]. Basically, it is an extension of graph theory [10], focusing on the modeling, representation, characterization, analysis and simulation ofcomplexsystemsbyconsideringmanyelementsandtheirinterconnections.C- plex networks concepts and methods have been used to study disease [17], tr- scription networks [5, 6, 4], protein-protein networks [22, 36, 16, 39], metabolic networks [23] and anatomy [40].

This book is dedicated to the atmosphere of our planet, and discusses historical and contemporary achievements in meteorological science and technology for the betterment of society. The book explores many significant atmospheric phenomena and physical processes from the local to global scale, as well as from the perspective of short and long-term time scales, and links these processes to various applications in other scientific disciplines with linkages to meteorology. In addition to addressing general topics such as climate system dynamics and climate change, the book also discusses atmospheric boundary layer, atmospheric waves, atmospheric chemistry, optics/photometeors, electricity, atmospheric modeling and numeric weather prediction. Through its interdisciplinary approach, the book will be of interest to researchers, students and academics in meteorology and atmospheric science, environmental physics, climate change dynamics, air pollution and human health impacts of atmospheric aerosols.

This is the first biography of Julian Schwinger, one of the great theoretical physicists of the twentieth century. A long-time colleague and collaborator of Richard Feynman, he was the joint winner with Feynman of the 1965 Nobel Prize for Physics for their work on quantum electrodynamics. However his contribution extended far beyond this, and his life and achievements are chronicled in this book.

Oligopoly theory is one of the most intensively studied areas of mathematical economics. On the basis of the pioneering works of Cournot (1838), many res- rchers have developed and extensively examined the different variants of oligopoly models. Initially, the existence and uniqueness of the equilibrium of the different types of oligopolies was the main concern, and later the dynamic extensions of these models became the focus. The classical result of Theocharis (1960) asserts that under discrete time scales and static expectations, the equilibrium of a sing- product oligopoly without product differentiation and with linear price and cost functions is asymptotically stable if and only if it is a duopoly. In the continuous time case, asymptotic stability is guaranteed for any number of ?rms. In these cases the resulting dynamical systems are also linear, where local and global asymptotic stability are equivalent to each other. The classical book of Okuguchi (1976) gives a comprehensive summary of the earlier results and developments. The multipr- uct extensionshave been discussed in Okuguchiand Szidarovszky(1999);however, nonlinear features were barely touched upon in these contributions. WiththedevelopmentofthecriticalcurvemethodbyGumowskiandMira(1980) (see also Mira et al. (1996))fordiscrete time systemsand the introductionof cont- uously distributed information lags by Invernizzi and Medio (1991) in continuous time systems, increasing attention has been given to the global dynamics of n- linear oligopolies. The authors of this book have devoted a great deal of research effort to this area.

The Future of Decentralized Electricity Distribution Networks assesses the evolution of the services delivered by the distribution network as the demands placed on it proliferates from distributed, self-generating, power storing and power sharing 'consumers' - which Sioshansi terms 'prosumagers'. The work outlines the processes by which passive and homogeneous electricity consumers become prosumers and prosumagers, the nature of their service needs and dependence on the services delivered by the distribution network diverges. Contributors assess how consumers are discovering and exercising options to migrate away from total reliance on upstream generators to produce electricity and on the delivery network for its transmission. As they do so, the "utilities" - be they distributors or retailers - must rethink the traditional utility business model. How will they find sufficient revenues to cover their fixed and variable costs as volumetric consumption declines when some consumers become prosumers - or go a step further and become prosumagers? This work argues that new service and business models, and new methods for collecting sufficient revenues to maintain the network, are mandatory for the survival of modern utilities.

This book investigates phase transitions and critical phenomena in disordered systems driven out of equilibrium. First, the author derives a dimensional reduction property that relates the long-distance physics of driven disordered systems to that of lower dimensional pure systems. By combining this property with a modern renormalization group technique, the critical behavior of random field spin models driven at a uniform velocity is subsequently investigated. The highlight of this book is that the driven random field XY model is shown to exhibit the Kosterlitz-Thouless transition in three dimensions. This is the first example of topological phase transitions in which the competition between quenched disorder and nonequilibrium driving plays a crucial role. The book also includes a pedagogical review of a renormalizaion group technique for disordered systems.