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Mathematical Physics in One Dimension: Exactly Soluble Models of Interacting Particles covers problems of mathematical physics with one-dimensional analogs. The book discusses classical statistical mechanics and phase transitions; the disordered chain of harmonic oscillators; and electron energy bands in ordered and disordered crystals. The text also describes the many-fermion problem; the theory of the interacting boson gas; the theory of the antiferromagnetic linear chains; and the time-dependent phenomena of many-body systems (i.e., classical or quantum-mechanical dynamics). Physicists and mathematicians will find the book invaluable.
This volume presents in a pedagogical yet complete way correlated systems in one dimension. After an introduction to the basic concepts of correlated systems, it gives a step-by-step description of the techniques needed to treat one dimension, and discusses the resulting physics.
One of the key components of modern physics, quantum mechanics is used in such fields as chemistry, electrical engineering, and computer science. Central to quantum mechanics is Schrödinger's Equation, which explains the behavior of atomic particles and the energy levels of a quantum system. Robert Gilmore's innovative approach to Schrödinger's Equation offers new insight into quantum mechanics at an elementary level. Gilmore presents compact transfer matrix methods for solving quantum problems that can easily be implemented on a personal computer. He shows how to use these methods on a large variety of potentials, both simple and periodic. He shows how to compute bound states, scattering states, and energy bands and describes the relation between bound and scattering states. Chapters on alloys, superlattices, quantum engineering, and solar cells indicate the practical application of the methods discussed. Gilmore's concise and elegant treatment will be of interest to students and professors of introductory and intermediate quantum courses, as well as professionals working in electrical engineering and applied mathematics.
"This introductory, algebra-based, two-semester college physics book is grounded with real-world examples, illustrations, and explanations to help students grasp key, fundamental physics concepts. ... This online, fully editable and customizable title includes learning objectives, concept questions, links to labs and simulations, and ample practice opportunities to solve traditional physics application problems."--Website of book.
Although the problem of a metal in one dimension has long been known to solid-state physicists, it was not until the synthesis of real one-dimensional or quasi-one-dimensional systems that this subject began to attract considerable attention. This has been due in part to the search for high temperature superconductivity and the possibility of reaching this goal with quasi-one-dimensional substances. A period of intense activity began in 1973 with the report of a measurement of an apparently divergent conduc tivity peak in TfF-TCNQ. Since then a great deal has been learned about quasi-one-dimensional conductors. The emphasis now has shifted from trying to find materials of very high conductivity to the many interesting problems of physics and chemistry involved. But many questions remain open and are still under active investigation. This book gives a review of the experimental as well as theoretical progress made in this field over the last years. All the chapters have been written by scientists who have established themselves as experts in theoreti cal and experimental solid-state physics. The book is intended to be of use both to students and researchers entering the field as well as to more advanced physicists. The wealth of ideas and information it contains ought to be useful to anyone interested in quasi-one-dimensional systems, organic solids, or the search for novel conduction and superconduction mechanisms. The editors are very grateful to the authors for their collaboration in this book.
In 1966, E.H. Lieb and D.C. r1attis published a book on "Mathematical Physics in One Dimension" [Academic Press, New York and London] which is much more than just a collection of reprints and which in fact marked the beginnings of the rapidly growing interest in one-dimensional problems and materials in the 1970's. In their Foreword, Lieb and r~attis made the observation that " ... there now exists a vast literature on this subject, albeit one which is not indexed under the topic "one dimension" in standard indexing journals and which is therefore hard to research ... ". Today, the situation is even worse, and we hope that these Proceedings will be a valuable guide to some of the main current areas of one-dimensional physics. From a theoretical point of view, one-dimensional problems have always been very attractive. Many non-trivial models are soluble in one dimension, while they are only approximately understood in three dimensions. Therefore, the corresponding exact solutions serve as a useful test of approximate ma thematical methods, and certain features of the one-dimensional solution re main relevant in higher dimensions. On the other hand, many important phe nomena are strongly enhanced, and many concepts show up especially clearly in one-dimensional or quasi -one-dimensional systems. Among them are the ef fects of fluctuations, of randomness, and of nonlinearity; a number of in teresting consequences are specific to one dimension.
This book introduces the reader to basic notions of integrable techniques for one-dimensional quantum systems. In a pedagogical way, a few examples of exactly solvable models are worked out to go from the coordinate approach to the Algebraic Bethe Ansatz, with some discussion on the finite temperature thermodynamics. The aim is to provide the instruments to approach more advanced books or to allow for a critical reading of research articles and the extraction of useful information from them. We describe the solution of the anisotropic XY spin chain; of the Lieb-Liniger model of bosons with contact interaction at zero and finite temperature; and of the XXZ spin chain, first in the coordinate and then in the algebraic approach. To establish the connection between the latter and the solution of two dimensional classical models, we also introduce and solve the 6-vertex model. Finally, the low energy physics of these integrable models is mapped into the corresponding conformal field theory. Through its style and the choice of topics, this book tries to touch all fundamental ideas behind integrability and is meant for students and researchers interested either in an introduction to later delve in the advance aspects of Bethe Ansatz or in an overview of the topic for broadening their culture.
Self-contained and up-to-date guide to one-dimensional reactions, dynamics, diffusion and adsorption.
This book presents an account of the exact solution of the Hubbard model in one dimension. The early chapters develop a self-contained introduction to Bethe's ansatz and its application to the one-dimensional Hubbard model. The later chapters address more advanced topics.
Provides an overview of the eigenspinors of the charge conjugation operator and mass one dimension fermions.