Group Theory In Solid State Physics And Photonics
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Group Theory In Solid State Physics And Photonics
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Author : Wolfram Hergert
language : en
Publisher: Wiley-VCH
Release Date : 2018-05-18
Group Theory In Solid State Physics And Photonics written by Wolfram Hergert and has been published by Wiley-VCH this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-05-18 with Photonics categories.
While group theory and its application to solid state physics is well established, this textbook raises two completely new aspects. First, it provides a better understanding by focusing on problem solving and making extensive use of Mathematica tools to visualize the concepts. Second, it offers a new tool for the photonics community by transferring the concepts of group theory and its application to photonic crystals. Clearly divided into three parts, the first provides the basics of group theory. Even at this stage, the authors go beyond the widely used standard examples to show the broad field of applications. Part II is devoted to applications in condensed matter physics, i.e. the electronic structure of materials. Combining the application of the computer algebra system Mathematica with pen and paper derivations leads to a better and faster understanding. The exhaustive discussion shows that the basics of group theory can also be applied to a totally different field, as seen in Part III. Here, photonic applications are discussed in parallel to the electronic case, with the focus on photonic crystals in two and three dimensions, as well as being partially expanded to other problems in the field of photonics. The authors have developed Mathematica package GTPack which is available for download from the book's homepage. Analytic considerations, numerical calculations and visualization are carried out using the same software. While the use of the Mathematica tools are demonstrated on elementary examples, they can equally be applied to more complicated tasks resulting from the reader's own research.
Group Theory In Solid State Physics And Photonics
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Author : Wolfram Hergert
language : en
Publisher: John Wiley & Sons
Release Date : 2018-04-20
Group Theory In Solid State Physics And Photonics written by Wolfram Hergert and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-04-20 with Science categories.
While group theory and its application to solid state physics is well established, this textbook raises two completely new aspects. First, it provides a better understanding by focusing on problem solving and making extensive use of Mathematica tools to visualize the concepts. Second, it offers a new tool for the photonics community by transferring the concepts of group theory and its application to photonic crystals. Clearly divided into three parts, the first provides the basics of group theory. Even at this stage, the authors go beyond the widely used standard examples to show the broad field of applications. Part II is devoted to applications in condensed matter physics, i.e. the electronic structure of materials. Combining the application of the computer algebra system Mathematica with pen and paper derivations leads to a better and faster understanding. The exhaustive discussion shows that the basics of group theory can also be applied to a totally different field, as seen in Part III. Here, photonic applications are discussed in parallel to the electronic case, with the focus on photonic crystals in two and three dimensions, as well as being partially expanded to other problems in the field of photonics. The authors have developed Mathematica package GTPack which is available for download from the book's homepage. Analytic considerations, numerical calculations and visualization are carried out using the same software. While the use of the Mathematica tools are demonstrated on elementary examples, they can equally be applied to more complicated tasks resulting from the reader's own research.
Group Theory
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Author : Mildred S. Dresselhaus
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-12-13
Group Theory written by Mildred S. Dresselhaus and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-12-13 with Science categories.
This concise, class-tested book was refined over the authors’ 30 years as instructors at MIT and the University Federal of Minas Gerais (UFMG) in Brazil. The approach centers on the conviction that teaching group theory along with applications helps students to learn, understand and use it for their own needs. Thus, the theoretical background is confined to introductory chapters. Subsequent chapters develop new theory alongside applications so that students can retain new concepts, build on concepts already learned, and see interrelations between topics. Essential problem sets between chapters aid retention of new material and consolidate material learned in previous chapters.
Space Group Representations
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Author : Nikolai B. Melnikov
language : en
Publisher: Springer Nature
Release Date : 2023-01-01
Space Group Representations written by Nikolai B. Melnikov and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-01-01 with Science categories.
This book is devoted to the construction of space group representations, their tabulation, and illustration of their use. Representation theory of space groups has a wide range of applications in modern physics and chemistry, including studies of electron and phonon spectra, structural and magnetic phase transitions, spectroscopy, neutron scattering, and superconductivity. The book presents a clear and practical method of deducing the matrices of all irreducible representations, including double-valued, and tabulates the matrices of irreducible projective representations for all 32 crystallographic point groups. One obtains the irreducible representations of all 230 space groups by multiplying the matrices presented in these compact and convenient to use tables by easily computed factors. A number of applications to the electronic band structure calculations are illustrated through real-life examples of different crystal structures. The book's content is accessible to both graduate and advanced undergraduate students with elementary knowledge of group theory and is useful to a wide range of experimentalists and theorists in materials and solid-state physics.
Symmetry And Condensed Matter Physics
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Author : M. El-Batanouny
language : en
Publisher: Cambridge University Press
Release Date : 2008-03-13
Symmetry And Condensed Matter Physics written by M. El-Batanouny and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-03-13 with Science categories.
Unlike existing texts, this book blends for the first time three topics in physics - symmetry, condensed matter physics and computational methods - into one pedagogical textbook. It includes new concepts in mathematical crystallography; experimental methods capitalizing on symmetry aspects; non-conventional applications such as Fourier crystallography, color groups, quasicrystals and incommensurate systems; as well as concepts and techniques behind the Landau theory of phase transitions. Adopting a computational approach to the application of group theoretical techniques to solving symmetry related problems, it dramatically alleviates the need for intensive calculations usually found in the presentation of symmetry. Writing computer programs helps the student achieve a firm understanding of the underlying concepts, and sample programs, based on Mathematica, are presented throughout the book. Containing over 150 exercises, this textbook is ideal for graduate students in condensed matter physics, materials science, and chemistry. Solutions and computer programs are available online at www.cambridge.org/9780521828451.
Applications Of Group Theory To Atoms Molecules And Solids
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Author : Thomas Wolfram
language : en
Publisher: Cambridge University Press
Release Date : 2014-01-09
Applications Of Group Theory To Atoms Molecules And Solids written by Thomas Wolfram and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-01-09 with Mathematics categories.
An applications-oriented approach gives graduate students and researchers in the physical sciences the tools needed to analyze any physical system.
Extreme Photonics Applications
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Author : Trevor Hall
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-12-11
Extreme Photonics Applications written by Trevor Hall and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-12-11 with Technology & Engineering categories.
"Extreme Photonics & Applications" arises from the 2008 NATO Advanced Study Institute in Laser Control & Monitoring in New Materials, Biomedicine, Environment, Security and Defense. Leading experts in the manipulation of light offered by recent advances in laser physics and nanoscience were invited to give lectures in their fields of expertise and participate in discussions on current research, applications and new directions. The sum of their contributions to this book is a primer for the state of scientific knowledge and the issues within the subject of photonics taken to the extreme frontiers: molding light at the ultra-finest scales, which represents the beginning of the end to limitations in optical science for the benefit of 21st Century technological societies. Laser light is an exquisite tool for physical and chemical research. Physicists have recently developed pulsed lasers with such short durations that one laser shot takes the time of one molecular vibration or one electron rotation in an atom, which makes it possible to observe their internal electronic structure, thereby enabling the study of physical processes and new chemical reactions. In parallel, advances in micro- and nano-structured photonic materials allow the precise manipulation of light on its natural scale of a wavelength. Photonic crystals, plasmons and related metamaterials - composed of subwavelength nanostructures - permit the manipulation of their dispersive properties and have allowed the experimental confirmation of bizarre new effects such as slow light and negative refraction. These advances open a vista on a new era in which it is possible to build lasers and engineer materials to control and use photons as precisely as it is already possible to do with electrons. http://www.photonics.uottawa.ca/nato-asi-2008/
Physics Of The Lorentz Group
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Author : Sibel Baskal
language : en
Publisher: Morgan & Claypool Publishers
Release Date : 2015-11-01
Physics Of The Lorentz Group written by Sibel Baskal and has been published by Morgan & Claypool Publishers this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-11-01 with Science categories.
This book explains the Lorentz mathematical group in a language familiar to physicists. While the three-dimensional rotation group is one of the standard mathematical tools in physics, the Lorentz group of the four-dimensional Minkowski space is still very strange to most present-day physicists. It plays an essential role in understanding particles moving at close to light speed and is becoming the essential language for quantum optics, classical optics, and information science. The book is based on papers and books published by the authors on the representations of the Lorentz group based on harmonic oscillators and their applications to high-energy physics and to Wigner functions applicable to quantum optics. It also covers the two-by-two representations of the Lorentz group applicable to ray optics, including cavity, multilayer and lens optics, as well as representations of the Lorentz group applicable to Stokes parameters and the Poincaré sphere on polarization optics.
Photonic Crystals
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Author : John D. Joannopoulos
language : en
Publisher: Princeton University Press
Release Date : 2011-10-30
Photonic Crystals written by John D. Joannopoulos and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-10-30 with Science categories.
Since it was first published in 1995, Photonic Crystals has remained the definitive text for both undergraduates and researchers on photonic band-gap materials and their use in controlling the propagation of light. This newly expanded and revised edition covers the latest developments in the field, providing the most up-to-date, concise, and comprehensive book available on these novel materials and their applications. Starting from Maxwell's equations and Fourier analysis, the authors develop the theoretical tools of photonics using principles of linear algebra and symmetry, emphasizing analogies with traditional solid-state physics and quantum theory. They then investigate the unique phenomena that take place within photonic crystals at defect sites and surfaces, from one to three dimensions. This new edition includes entirely new chapters describing important hybrid structures that use band gaps or periodicity only in some directions: periodic waveguides, photonic-crystal slabs, and photonic-crystal fibers. The authors demonstrate how the capabilities of photonic crystals to localize light can be put to work in devices such as filters and splitters. A new appendix provides an overview of computational methods for electromagnetism. Existing chapters have been considerably updated and expanded to include many new three-dimensional photonic crystals, an extensive tutorial on device design using temporal coupled-mode theory, discussions of diffraction and refraction at crystal interfaces, and more. Richly illustrated and accessibly written, Photonic Crystals is an indispensable resource for students and researchers. Extensively revised and expanded Features improved graphics throughout Includes new chapters on photonic-crystal fibers and combined index-and band-gap-guiding Provides an introduction to coupled-mode theory as a powerful tool for device design Covers many new topics, including omnidirectional reflection, anomalous refraction and diffraction, computational photonics, and much more.
Group Theory And Physics
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Author : Shlomo Sternberg
language : en
Publisher: Cambridge University Press
Release Date : 1995-09-07
Group Theory And Physics written by Shlomo Sternberg and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995-09-07 with Mathematics categories.
This textbook, based on courses taught at Harvard University, is an introduction to group theory and its application to physics. The physical applications are considered as the mathematical theory is developed so that the presentation is unusually cohesive and well-motivated. Many modern topics are dealt with, and there is much discussion of the group SU(n) and its representations. This is of great significance in elementary particle physics. Applications to solid state physics are also considered. This stimulating account will prove to be an essential resource for senior undergraduate students and their teachers.