Download or read book Pt Symmetry In Quantum And Classical Physics written by Carl M Bender and published by World Scientific Publishing. This book was released on 2018-11-22 with total page 469 pages. Available in PDF, EPUB and Kindle. Book excerpt: 'The text is easy to read because the matter is clearly explained. Symmetries are a central component of physical laws, and the PT-symmetry proves to be very interesting and fruitful. The discussion of the matter is up-to-date and self-contained. The book is recommended to students of higher courses, PhD and researchers. It is also a basic read to those who wish to have an insight into this field.'Contemporary PhysicsOriginated by the author in 1998, the field of PT (parity-time) symmetry has become an extremely active and exciting area of research. PT-symmetric quantum and classical systems have theoretical, experimental, and commercial applications, and have been the subject of many journal articles, PhD theses, conferences, and symposia. Carl Bender's work has influenced major advances in physics and generations of students.This book is an accessible entry point to PT symmetry, ideal for students and scientists looking to begin their own research projects in this field.

Download or read book PT Symmetry in Quantum and Classical Physics written by Carl M. Bender and published by . This book was released on 2018 with total page 469 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Supersymmetry In Quantum and Classical Mechanics written by Bijan Kumar Bagchi and published by CRC Press. This book was released on 2000-09-21 with total page 242 pages. Available in PDF, EPUB and Kindle. Book excerpt: Following Witten's remarkable discovery of the quantum mechanical scheme in which all the salient features of supersymmetry are embedded, SCQM (supersymmetric classical and quantum mechanics) has become a separate area of research . In recent years, progress in this field has been dramatic and the literature continues to grow. Until now, no book has offered an overview of the subject with enough detail to allow readers to become rapidly familiar with its key ideas and methods. Supersymmetry in Classical and Quantum Mechanics offers that overview and summarizes the major developments of the last 15 years. It provides both an up-to-date review of the literature and a detailed exposition of the underlying SCQM principles. For those just beginning in the field, the author presents step-by-step details of most of the computations. For more experienced readers, the treatment includes systematic analyses of more advanced topics, such as quasi- and conditional solvability and the role of supersymmetry in nonlinear systems.

Download or read book Symmetries in Quantum Mechanics and Statistical Physics written by Georg Junker and published by Mdpi AG. This book was released on 2021-12-27 with total page 164 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book collects contributions to the Special Issue entitled "Symmetries in Quantum Mechanics and Statistical Physics" of the journal Symmetry. These contributions focus on recent advancements in the study of PT-invariance of non-Hermitian Hamiltonians, the supersymmetric quantum mechanics of relativistic and non-relativisitc systems, duality transformations for power-law potentials and conformal transformations. New aspects on the spreading of wave packets are also discussed.

Download or read book Non Hermitian Quantum Mechanics written by Nimrod Moiseyev and published by Cambridge University Press. This book was released on 2011-02-17 with total page 409 pages. Available in PDF, EPUB and Kindle. Book excerpt: Non-Hermitian quantum mechanics (NHQM) is an important alternative to the standard (Hermitian) formalism of quantum mechanics, enabling the solution of otherwise difficult problems. The first book to present this theory, it is useful to advanced graduate students and researchers in physics, chemistry and engineering. NHQM provides powerful numerical and analytical tools for the study of resonance phenomena - perhaps one of the most striking events in nature. It is especially useful for problems whose solutions cause extreme difficulties within the structure of a conventional Hermitian framework. NHQM has applications in a variety of fields, including optics, where the refractive index is complex; quantum field theory, where the parity-time (PT) symmetry properties of the Hamiltonian are investigated; and atomic and molecular physics and electrical engineering, where complex potentials are introduced to simplify numerical calculations.

Download or read book Principles of Quantum Mechanics written by R. Shankar and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 676 pages. Available in PDF, EPUB and Kindle. Book excerpt: R. Shankar has introduced major additions and updated key presentations in this second edition of Principles of Quantum Mechanics. New features of this innovative text include an entirely rewritten mathematical introduction, a discussion of Time-reversal invariance, and extensive coverage of a variety of path integrals and their applications. Additional highlights include: - Clear, accessible treatment of underlying mathematics - A review of Newtonian, Lagrangian, and Hamiltonian mechanics - Student understanding of quantum theory is enhanced by separate treatment of mathematical theorems and physical postulates - Unsurpassed coverage of path integrals and their relevance in contemporary physics The requisite text for advanced undergraduate- and graduate-level students, Principles of Quantum Mechanics, Second Edition is fully referenced and is supported by many exercises and solutions. The book’s self-contained chapters also make it suitable for independent study as well as for courses in applied disciplines.

Download or read book Physics from Symmetry written by Jakob Schwichtenberg and published by Springer. This book was released on 2017-12-01 with total page 294 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a textbook that derives the fundamental theories of physics from symmetry. It starts by introducing, in a completely self-contained way, all mathematical tools needed to use symmetry ideas in physics. Thereafter, these tools are put into action and by using symmetry constraints, the fundamental equations of Quantum Mechanics, Quantum Field Theory, Electromagnetism, and Classical Mechanics are derived. As a result, the reader is able to understand the basic assumptions behind, and the connections between the modern theories of physics. The book concludes with first applications of the previously derived equations. Thanks to the input of readers from around the world, this second edition has been purged of typographical errors and also contains several revised sections with improved explanations.

Download or read book All Dielectric Nanophotonics written by Alexander S. Shalin and published by Elsevier. This book was released on 2023-11-09 with total page 430 pages. Available in PDF, EPUB and Kindle. Book excerpt: All-Dielectric Nanophotonics aims to review the underlying principles, advances and future directions of research in the field. The book reviews progress in all-dielectric metasurfaces and nanoantennas, new types of excitations, such as magnetic and toroidal modes and associated anapole states. Ultrahigh-Q resonant modes such as bound states in the continuum are covered and the promise of replacing conventional bulky optical elements with nanometer-scale structures with enhanced functionality is discussed. This book is suitable for new entrants to the field as an overview of this research area. Experienced researchers and professionals in the field may also find this book suitable as a reference. - Provides an overview of the fundamental principles, theories and calculation techniques underpinning all-dielectric nanophotonics research - Reviews current progress in the field, such as all-dielectric metasurfaces and nanoantennas, new types of excitations, associated anapole states, and more - Discusses emerging applications such as active nanophotonics with in-depth analysis

Download or read book Parity time Symmetry and Its Applications written by Demetrios Christodoulides and published by Springer. This book was released on 2018-11-28 with total page 585 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers a comprehensive review of the state-of-the-art theoretical and experimental advances in linear and nonlinear parity-time-symmetric systems in various physical disciplines, and surveys the emerging applications of parity-time (PT) symmetry. PT symmetry originates from quantum mechanics, where if the Schrodinger operator satisfies the PT symmetry, then its spectrum can be all real. This concept was later introduced into optics, Bose-Einstein condensates, metamaterials, electric circuits, acoustics, mechanical systems and many other fields, where a judicious balancing of gain and loss constitutes a PT-symmetric system. Even though these systems are dissipative, they exhibit many signature properties of conservative systems, which make them mathematically and physically intriguing. Important PT-symmetry applications have also emerged. This book describes the latest advances of PT symmetry in a wide range of physical areas, with contributions from the leading experts. It is intended for researchers and graduate students to enter this research frontier, or use it as a reference book.

Download or read book Symmetries in Physics written by Katherine Brading and published by Cambridge University Press. This book was released on 2003-12-04 with total page 459 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book brings together philosophical discussions of symmetry in physics, highlighting the main issues and controversies. It covers all the fundamental symmetries of modern physics, as well as discussing symmetry-breaking and general interpretational issues. For each topic, classic texts are followed by review articles and short commentaries.

Download or read book Advances in Functional Analysis and Operator Theory written by Marat V. Markin and published by American Mathematical Society. This book was released on 2024-04-09 with total page 250 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of the AMS-EMS-SMF Special Session on Advances in Functional Analysis and Operator Theory, held July 18–22, 2022, at the Université de Grenoble-Alpes, Grenoble, France. The papers reflect the modern interplay between differential equations, functional analysis, operator algebras, and their applications from the dynamics to quantum groups to number theory. Among the topics discussed are the Sturm-Liouville and boundary value problems, axioms of quantum mechanics, $C^{*}$-algebras and symbolic dynamics, von Neumann algebras and low-dimensional topology, quantum permutation groups, the Jordan algebras, and the Kadison–Singer transforms.

Download or read book Differential Geometry Through Supersymmetric Glasses written by Andrei Smilga and published by World Scientific. This book was released on 2020-06-16 with total page 346 pages. Available in PDF, EPUB and Kindle. Book excerpt: Back in 1982, Edward Witten noticed that classical problems of differential geometry and differential topology such as the de Rham complex and Morse theory can be described in a very simple and transparent way using the language of supersymmetric quantum mechanics. Since then, many research papers have been written on this subject. Unfortunately not all the results in this field known to mathematicians have obtained a transparent physical interpretation, even if this new physical technique has also allowed many mathematical results to be derived which are completely new, in particular, hyper-Kaehler and the so-called HKT geometry. But in almost 40 years, no comprehensive monograph has appeared on this subject. So this book written by an expert in supersymmetric quantum field theories, supersymmetric quantum mechanics and its geometrical applications, addresses this yearning gap.It comprises three parts: The first, GEOMETRY, gives basic information on the geometry of real, complex, hyper-Kaehler and HKT manifolds, and is principally addressed to the physicist. The second part 'PHYSICS' presents information on classical mechanics with ordinary and Grassmann dynamics variables. Besides, the author introduces supersymmetry and dwells in particular on the representation of supersymmetry algebra in superspace. And the last and most important part of the book 'SYNTHESIS', is where the ideas borrowed from physics are used to study purely mathematical phenomena.

Download or read book Applied Quantum Mechanics written by Walter Ashley Harrison and published by World Scientific. This book was released on 2000 with total page 376 pages. Available in PDF, EPUB and Kindle. Book excerpt: Quantum mechanics is widely recognized as the basic law which governs all of nature, including all materials and devices. It has always been essential to the understanding of material properties, and as devices become smaller it is also essential for studying their behavior. Nevertheless, only a small fraction of graduate engineers and materials scientists take a course giving a systematic presentation of the subject. The courses for physics students tend to focus on the fundamentals and formal background, rather than on application, and do not fill the need. This invaluable text has been designed to fill the very apparent gap.The book covers those parts of quantum theory which may be necessary for a modern engineer. It focuses on the approximations and concepts which allow estimates of the entire range of properties of nuclei, atoms, molecules, and solids, as well as the behavior of lasers and other quantum-optic devices. It may well prove useful also to graduate students in physics, whose courses on quantum theory tend not to include any of these applications. The material has been the basis of a course taught to graduate engineering students for the past four years at Stanford University.Topics Discussed: Foundations; Simple Systems; Hamiltonian Mechanics; Atoms and Nuclei; Molecules; Crystals; Transitions; Tunneling; Transition Rates; Statistical Mechanics; Transport; Noise; Energy Bands; Electron Dynamics in Solids; Vibrations in Solids; Creation and Annihilation Operators; Phonons; Photons and Lasers; Coherent States; Coulomb Effects; Cooperative Phenomena; Magnetism; Shake-off Excitations; Exercise Problems.

Download or read book The Semiclassical Way to Dynamics and Spectroscopy written by Eric J. Heller and published by Princeton University Press. This book was released on 2018-06-05 with total page 473 pages. Available in PDF, EPUB and Kindle. Book excerpt: A graduate-level text that examines the semiclassical approach to quantum mechanics Physical systems have been traditionally described in terms of either classical or quantum mechanics. But in recent years, semiclassical methods have developed rapidly, providing deep physical insight and computational tools for quantum dynamics and spectroscopy. In this book, Eric Heller introduces and develops this subject, demonstrating its power with many examples. In the first half of the book, Heller covers relevant aspects of classical mechanics, building from them the semiclassical way through the semiclassical limit of the Feynman path integral. The second half of the book applies this approach to various kinds of spectroscopy, such as molecular spectroscopy and electron imaging and quantum dynamical systems with an emphasis on tunneling. Adopting a distinctly time-dependent viewpoint, Heller argues for semiclassical theories from experimental and theoretical vantage points valuable to research in physics and chemistry. Featuring more than two hundred figures, the book provides a geometric, phase-space, and coordinate-space pathway to greater understanding. Filled with practical examples and applications, The Semiclassical Way to Dynamics and Spectroscopy is a comprehensive presentation of the tools necessary to successfully delve into this unique area of quantum mechanics. A comprehensive approach for using classical mechanics to do quantum mechanics More than two hundred figures to assist intuition Emphasis on semiclassical Green function and wave packet perspective, as well as tunneling and spectroscopy Chapters include quantum mechanics of classically chaotic systems, quantum scarring, and other modern dynamical topics

Download or read book Witten Index written by Andrei Smilga and published by World Scientific. This book was released on 2024-08-27 with total page 322 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book is devoted to vacuum structure of supersymmetric quantum mechanical and field theories. The Witten Index (the title of book) is a powerful theoretical tool, which allows one to find out whether supersymmetry breaks down spontaneously in a given theory or not. This is the main physical interest of this notion, but the latter has also many beautiful purely mathematical connotations. It represents a variant of the so-called equivariant index introduced by Cartan back in 1950 and is closely related to the Atiyah-Singer index.In his previous book 'Differential Geometry through Supersymmetric Glasses', World Scientific, 2020, the author showed how the supersymmetric language allows one to describe, in a rather transparent way, some known facts of differential geometry and also derive new results in this field.This book is mostly addressed to experts in quantum field theory, but the first three chapters has an introductory textbook nature and can be read by a non-expert. In Chapters 4 and 5, the general aspects of the Witten index are explained and the relationship with pure mathematical problems is elucidated. Chapters 6, 7, 8 are devoted to four-dimensional supersymmetric gauge theories: pure supersymmetric Yang-Mills theories in Chapter 6, the theories including a nonchiral (Chapter 7) and chiral (Chapter 8) matter. Chapter 9 is devoted to the so-called maximal supersymmetric quantum mechanics obtained by a dimensional reduction of the 10-dimensional supersymmetric Yang-Mills theory. In Chapter 10, the numbers of supersymmetric vacua in 3-dimensional supersymmetric Yang-Mills-Chern-Simons theories is calculated. Finally, in Chapter 11, the author discusses some relatives of the Witten index, such as the indices for the 4-dimensional theories compactified on S3 x R, rather than 4-torus or the so-called Cecolli-Fendley-Intriligator-Vafa index.

Download or read book Pseudo Bosons and Their Coherent States written by Fabio Bagarello and published by Springer Nature. This book was released on 2022-04-22 with total page 208 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is based on the analysis of canonical commutation relations (CCRs) and their possible deformations. In light of the recent interest on PT-quantum mechanics, the author presents a special deformed version of the CCRs, and discusses the consequences of this deformation both from a mathematical side, and for its possible applications to physics. These include the analysis of several non self-adjoint Hamiltonians, a novel view to the position and momentum operators, and a general approach to compute path integrals and transition probabilities using the so-called bi-coherent states. The book is meant for researchers and is also suited for advanced students. It can be used as a gentle introduction to some delicate aspects in functional analysis and in quantum mechanics for non self-adjoint observables.

Download or read book Trails in Modern Theoretical and Mathematical Physics written by Andrea Cintio and published by Springer Nature. This book was released on 2024-01-22 with total page 321 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book celebrates the life and work of the late Giovanni Morchio (1944–2021). It features scientific and anecdotal contributions written by his former colleagues, co-authors, and students, as well as senior scientists who were active witnesses to the dramatic advances in physics and in mathematics that took place during his 50-year-long career. The volume begins with a biographical introduction, detailing Giovanni Morchio’s life and his role as a physicist, mathematician, teacher, and scientist. The core of the book covers a vast spectrum of ideas, reflecting Dr Morchio’s scientific interests. Each chapter develops a specific topic of modern research, ranging from quantum mechanics and quantum field theory to additional themes such as the connection between general relativity and Newtonian gravitation. Every contribution provides a historical retrospective, a survey of advances, an outlook of future perspectives and challenges, and an updated bibliography. The last part collects the authors’ recollections of their professional and personal interactions with Dr Morchio, in recognition of his deep achievements, his exceptional pedagogical qualities, and his praiseworthy social and pro bono commitment. Authored by physicists of international calibre covering a broad range of subjects, the book will be a valuable reference for researchers and students of theoretical and mathematical physics.