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This book systematically introduces the nonlinear adiabatic evolution theory of quantum many-body systems. The nonlinearity stems from a mean-field treatment of the interactions between particles, and the adiabatic dynamics of the system can be accurately described by the nonlinear Schrödinger equation. The key points in this book include the adiabatic condition and adiabatic invariant for nonlinear system; the adiabatic nonlinear Berry phase; and the exotic virtual magnetic field, which gives the geometric meaning of the nonlinear Berry phase. From the quantum-classical correspondence, the linear and nonlinear comparison, and the single particle and interacting many-body difference perspectives, it shows a distinct picture of adiabatic evolution theory. It also demonstrates the applications of the nonlinear adiabatic evolution theory for various physical systems. Using simple models it illustrates the basic points of the theory, which are further employed for the solution of complex problems of quantum theory for many-particle systems. The results obtained are supplemented by numerical calculations, presented as tables and figures.
Berry phase has been widely used in condensed matter physics in the past two decades. This volume is a timely collection of essential papers in this important field, which is highlighted by 2016 Nobel Prize in physics and recent exciting developments in topological matters. Each chapter has an introduction, which helps readers to understand the reprints that follow.
In recent years nonlinear and irreversible quantum mechanics is becoming increasingly important because of the availability of precision experiments. There are new and successful attempts to understand quantum irreversibility. The development of generalized symmetries has to led to new families of evolution equations for pure and mixed states. On the one hand, this timely symposium covers nonlinear and irreversible quantum mechanics, the theory of quantization methods, causality and various problems important in this context. On the other hand, it reports the development of quantum group symmetries, and of methods to construct deformed quantum mechanical evolution equations like the q-deformed Schrödinger equations.
This book systematically introduces the nonlinear adiabatic evolution theory of quantum many-body systems. The nonlinearity stems from a mean-field treatment of the interactions between particles, and the adiabatic dynamics of the system can be accurately described by the nonlinear Schrödinger equation. The key points in this book include the adiabatic condition and adiabatic invariant for nonlinear system; the adiabatic nonlinear Berry phase; and the exotic virtual magnetic field, which gives the geometric meaning of the nonlinear Berry phase. From the quantum-classical correspondence, the linear and nonlinear comparison, and the single particle and interacting many-body difference perspectives, it shows a distinct picture of adiabatic evolution theory. It also demonstrates the applications of the nonlinear adiabatic evolution theory for various physical systems. Using simple models it illustrates the basic points of the theory, which are further employed for the solution of complex problems of quantum theory for many-particle systems. The results obtained are supplemented by numerical calculations, presented as tables and figures.
The field of isotope effects has expanded exponentially in the last decade, and researchers are finding isotopes increasingly useful in their studies. Bringing literature on the subject up to date, Isotope Effects in Chemistry and Biology covers current principles, methods, and a broad range of applications of isotope effects in the physical, biolo
The first reference of its kind in the rapidly emerging field of computational approachs to materials research, this is a compendium of perspective-providing and topical articles written to inform students and non-specialists of the current status and capabilities of modelling and simulation. From the standpoint of methodology, the development follows a multiscale approach with emphasis on electronic-structure, atomistic, and mesoscale methods, as well as mathematical analysis and rate processes. Basic models are treated across traditional disciplines, not only in the discussion of methods but also in chapters on crystal defects, microstructure, fluids, polymers and soft matter. Written by authors who are actively participating in the current development, this collection of 150 articles has the breadth and depth to be a major contributor toward defining the field of computational materials. In addition, there are 40 commentaries by highly respected researchers, presenting various views that should interest the future generations of the community. Subject Editors: Martin Bazant, MIT; Bruce Boghosian, Tufts University; Richard Catlow, Royal Institution; Long-Qing Chen, Pennsylvania State University; William Curtin, Brown University; Tomas Diaz de la Rubia, Lawrence Livermore National Laboratory; Nicolas Hadjiconstantinou, MIT; Mark F. Horstemeyer, Mississippi State University; Efthimios Kaxiras, Harvard University; L. Mahadevan, Harvard University; Dimitrios Maroudas, University of Massachusetts; Nicola Marzari, MIT; Horia Metiu, University of California Santa Barbara; Gregory C. Rutledge, MIT; David J. Srolovitz, Princeton University; Bernhardt L. Trout, MIT; Dieter Wolf, Argonne National Laboratory.
The 24 articles presented in this volume cover emerging areas in nonlinear dynamics. They discuss a range of topics, from chaotic quantum systems to nonlinear dynamics of the earth's magnetosphere and from microscopic chaos and nonequilibrium statistical mechanics to nonlinear dynamics of human brain activity. The articles are written by leading researchers both from India and other countries. It is hoped that the volume will provide information and inspiration, and suggest new research directions, both to the expert and novice alike.
This book presents an in-depth study of the discrete nonlinear Schrödinger equation (DNLSE), with particular emphasis on spatially small systems that permit analytic solutions. In many quantum systems of contemporary interest, the DNLSE arises as a result of approximate descriptions despite the fundamental linearity of quantum mechanics. Such scenarios, exemplified by polaron physics and Bose-Einstein condensation, provide application areas for the theoretical tools developed in this text. The book begins with an introduction of the DNLSE illustrated with the dimer, development of fundamental analytic tools such as elliptic functions, and the resulting insights into experiment that they allow. Subsequently, the interplay of the initial quantum phase with nonlinearity is studied, leading to novel phenomena with observable implications in fields such as fluorescence depolarization of stick dimers, followed by analysis of more complex and/or larger systems. Specific examples analyzed in the book include the nondegenerate nonlinear dimer, nonlinear trapping, rotational polarons, and the nonadiabatic nonlinear dimer. Phenomena treated include strong carrier-phonon interactions and Bose-Einstein condensation. This book is aimed at researchers and advanced graduate students, with chapter summaries and problems to test the reader’s understanding, along with an extensive bibliography. The book will be essential reading for researchers in condensed matter and low-temperature atomic physics, as well as any scientist who wants fascinating insights into the role of nonlinearity in quantum physics.
In the history of physics and science, quantum mechanics has served as the foundation of modern science. This book discusses the properties of microscopic particles in nonlinear systems, principles of the nonlinear quantum mechanical theory, and its applications in condensed matter, polymers and biological systems.The book is essentially composed of three parts. The first part presents a review of linear quantum mechanics, as well as theoretical and experimental fundamentals that establish the nonlinear quantum mechanical theory. The theory itself and its essential features are covered in the second part. In the final part, extensive applications of this theory in physics, biology and polymer are introduced. The whole volume forms a complete system of nonlinear quantum mechanics.The book is intended for researchers, graduate students as well as upper-level undergraduates.