Geometric Phases In Classical And Quantum Mechanics
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Geometric Phases In Classical And Quantum Mechanics
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Author : Dariusz Chruscinski
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Geometric Phases In Classical And Quantum Mechanics written by Dariusz Chruscinski 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 2012-12-06 with Mathematics categories.
Several well-established geometric and topological methods are used in this work in an application to a beautiful physical phenomenon known as the geometric phase. This book examines the geometric phase, bringing together different physical phenomena under a unified mathematical scheme. The material is presented so that graduate students and researchers in applied mathematics and physics with an understanding of classical and quantum mechanics can handle the text.
Geometric Phases In Classical And Quantum Mechanics
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Author : Dariusz Chruscinski
language : en
Publisher: Birkhäuser
Release Date : 2012-12-08
Geometric Phases In Classical And Quantum Mechanics written by Dariusz Chruscinski and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-08 with Mathematics categories.
Several well-established geometric and topological methods are used in this work in an application to a beautiful physical phenomenon known as the geometric phase. This book examines the geometric phase, bringing together different physical phenomena under a unified mathematical scheme. The material is presented so that graduate students and researchers in applied mathematics and physics with an understanding of classical and quantum mechanics can handle the text.
Geometric Phases In Classical And Quantum Mechanics
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Author : D. Chrus'cin'ski
language : en
Publisher:
Release Date : 2004
Geometric Phases In Classical And Quantum Mechanics written by D. Chrus'cin'ski and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with categories.
Geometric Phases In Physics
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Author : Alfred Shapere
language : en
Publisher: World Scientific
Release Date : 1989-07-01
Geometric Phases In Physics written by Alfred Shapere and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1989-07-01 with Mathematics categories.
During the last few years, considerable interest has been focused on the phase that waves accumulate when the equations governing the waves vary slowly. The recent flurry of activity was set off by a paper by Michael Berry, where it was found that the adiabatic evolution of energy eigenfunctions in quantum mechanics contains a phase of geometric origin (now known as ‘Berry's phase’) in addition to the usual dynamical phase derived from Schrödinger's equation. This observation, though basically elementary, seems to be quite profound. Phases with similar mathematical origins have been identified and found to be important in a startling variety of physical contexts, ranging from nuclear magnetic resonance and low-Reynolds number hydrodynamics to quantum field theory. This volume is a collection of original papers and reprints, with commentary, on the subject.
Analytic Hyperbolic Geometry And Albert Einstein S Special Theory Of Relativity
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Author : Abraham Albert Ungar
language : en
Publisher: World Scientific
Release Date : 2008-02-11
Analytic Hyperbolic Geometry And Albert Einstein S Special Theory Of Relativity written by Abraham Albert Ungar and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-02-11 with Mathematics categories.
This book presents a powerful way to study Einstein's special theory of relativity and its underlying hyperbolic geometry in which analogies with classical results form the right tool. It introduces the notion of vectors into analytic hyperbolic geometry, where they are called gyrovectors.Newtonian velocity addition is the common vector addition, which is both commutative and associative. The resulting vector spaces, in turn, form the algebraic setting for the standard model of Euclidean geometry. In full analogy, Einsteinian velocity addition is a gyrovector addition, which is both gyrocommutative and gyroassociative. The resulting gyrovector spaces, in turn, form the algebraic setting for the Beltrami-Klein ball model of the hyperbolic geometry of Bolyai and Lobachevsky. Similarly, Möbius addition gives rise to gyrovector spaces that form the algebraic setting for the Poincaré ball model of hyperbolic geometry.In full analogy with classical results, the book presents a novel relativistic interpretation of stellar aberration in terms of relativistic gyrotrigonometry and gyrovector addition. Furthermore, the book presents, for the first time, the relativistic center of mass of an isolated system of noninteracting particles that coincided at some initial time t = 0. The novel relativistic resultant mass of the system, concentrated at the relativistic center of mass, dictates the validity of the dark matter and the dark energy that were introduced by cosmologists as ad hoc postulates to explain cosmological observations about missing gravitational force and late-time cosmic accelerated expansion.The discovery of the relativistic center of mass in this book thus demonstrates once again the usefulness of the study of Einstein's special theory of relativity in terms of its underlying analytic hyperbolic geometry.
Artificial General Intelligence
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Author : Matthew Iklé
language : en
Publisher: Springer Nature
Release Date : 2025-08-06
Artificial General Intelligence written by Matthew Iklé and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-08-06 with Computers categories.
This book constitutes the refereed proceedings of the 18th International Conference on Artificial General Intelligence, AGI 2025, held in Reykjavic, Iceland in August 2025. The 72 full papers included in this book were carefully reviewed and selected from 179 submissions. They were organized in topical sections as follows: novel learning algorithms, reasoning systems, theoretical neurobiology and bio-inspired systems, quantum computing, theories of machine consciousness, ethics, safety, formal mathematical foundations and philosophy of AGI.
Trends In Quantum Computing Research
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Author : Susan Shannon
language : en
Publisher: Nova Publishers
Release Date : 2006
Trends In Quantum Computing Research written by Susan Shannon and has been published by Nova Publishers this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006 with Computers categories.
Quantum information processing is an exciting new emergent and interdisciplinary field. It combines questions of national security (When will today's public key cryptography be broken?) to questions of fundamental science (What are the fundamental limits to information processing?). It has thrived through the collaboration between the computer, engineering, mathematical and physical sciences. It is a field that is challenging our understanding of information, communication, computation, and of the fundamental laws of nature. This book brings together leading research in the field.
Introduction To Topological Quantum Matter Quantum Computation
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Author : Tudor D. Stanescu
language : en
Publisher: CRC Press
Release Date : 2016-12-19
Introduction To Topological Quantum Matter Quantum Computation written by Tudor D. Stanescu and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-12-19 with Science categories.
What is "topological" about topological quantum states? How many types of topological quantum phases are there? What is a zero-energy Majorana mode, how can it be realized in a solid state system, and how can it be used as a platform for topological quantum computation? What is quantum computation and what makes it different from classical computation? Addressing these and other related questions, Introduction to Topological Quantum Matter & Quantum Computation provides an introduction to and a synthesis of a fascinating and rapidly expanding research field emerging at the crossroads of condensed matter physics, mathematics, and computer science. Providing the big picture, this book is ideal for graduate students and researchers entering this field as it allows for the fruitful transfer of paradigms and ideas amongst different areas, and includes many specific examples to help the reader understand abstract and sometimes challenging concepts. It explores the topological quantum world beyond the well-known topological insulators and superconductors and emphasizes the deep connections with quantum computation. It addresses key principles behind the classification of topological quantum phases and relevant mathematical concepts and discusses models of interacting and noninteracting topological systems, such as the torric code and the p-wave superconductor. The book also covers the basic properties of anyons, and aspects concerning the realization of topological states in solid state structures and cold atom systems. Quantum computation is also presented using a broad perspective, which includes fundamental aspects of quantum mechanics, such as Bell's theorem, basic concepts in the theory of computation, such as computational models and computational complexity, examples of quantum algorithms, and elements of classical and quantum information theory.
Homogenization Of Partial Differential Equations
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Author : Vladimir A. Marchenko
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-12-22
Homogenization Of Partial Differential Equations written by Vladimir A. Marchenko 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 2008-12-22 with Mathematics categories.
Homogenization is a method for modeling processes in microinhomogeneous media, which are encountered in radiophysics, filtration theory, rheology, elasticity theory, and other domains of mechanics, physics, and technology. These processes are described by PDEs with rapidly oscillating coefficients or boundary value problems in domains with complex microstructure. From the technical point of view, given the complexity of these processes, the best techniques to solve a wide variety of problems involve constructing appropriate macroscopic (homogenized) models. The present monograph is a comprehensive study of homogenized problems, based on the asymptotic analysis of boundary value problems as the characteristic scales of the microstructure decrease to zero. The work focuses on the construction of nonstandard models: non-local models, multicomponent models, and models with memory. Along with complete proofs of all main results, numerous examples of typical structures of microinhomogeneous media with their corresponding homogenized models are provided. Graduate students, applied mathematicians, physicists, and engineers will benefit from this monograph, which may be used in the classroom or as a comprehensive reference text.
Physical Effects Of Geometric Phases
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Author : Qian Niu
language : en
Publisher: World Scientific
Release Date : 2017-08-28
Physical Effects Of Geometric Phases written by Qian Niu and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-08-28 with Science categories.
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.