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Tensor Network Contractions

Authors: --- --- --- --- et al.
Book Series: Lecture Notes in Physics ISBN: 9783030344894 Year: Pages: 150 DOI: 10.1007/978-3-030-34489-4 Language: English
Publisher: Springer Nature
Subject: Mathematics --- Computer Science
Added to DOAB on : 2020-02-04 11:21:17
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Tensor network is a fundamental mathematical tool with a huge range of applications in physics, such as condensed matter physics, statistic physics, high energy physics, and quantum information sciences. This open access book aims to explain the tensor network contraction approaches in a systematic way, from the basic definitions to the important applications. This book is also useful to those who apply tensor networks in areas beyond physics, such as machine learning and the big-data analysis. Tensor network originates from the numerical renormalization group approach proposed by K. G. Wilson in 1975. Through a rapid development in the last two decades, tensor network has become a powerful numerical tool that can efficiently simulate a wide range of scientific problems, with particular success in quantum many-body physics. Varieties of tensor network algorithms have been proposed for different problems. However, the connections among different algorithms are not well discussed or reviewed. To fill this gap, this book explains the fundamental concepts and basic ideas that connect and/or unify different strategies of the tensor network contraction algorithms. In addition, some of the recent progresses in dealing with tensor decomposition techniques and quantum simulations are also represented in this book to help the readers to better understand tensor network. This open access book is intended for graduated students, but can also be used as a professional book for researchers in the related fields. To understand most of the contents in the book, only basic knowledge of quantum mechanics and linear algebra is required. In order to fully understand some advanced parts, the reader will need to be familiar with notion of condensed matter physics and quantum information, that however are not necessary to understand the main parts of the book. This book is a good source for non-specialists on quantum physics to understand tensor network algorithms and the related mathematics.

Foundations of Quantum Theory: From Classical Concepts to Operator Algebras

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Book Series: Fundamental Theories of Physics ISSN: 0168-1222 ISBN: 9783319517773 Volume: 188 Pages: 861 DOI: http://dx.doi.org/10.1007/978-3-319-51777-3 Language: English
Publisher: Springer Nature
Subject: Physics (General)
Added to DOAB on : 2017-07-19 16:33:13
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This book studies the foundations of quantum theory through its relationship to classical physics. This idea goes back to the Copenhagen Interpretation (in the original version due to Bohr and Heisenberg), which the author relates to the mathematical formalism of operator algebras originally created by von Neumann. The book therefore includes comprehensive appendices on functional analysis and C*-algebras, as well as a briefer one on logic, category theory, and topos theory. Matters of foundational as well as mathematical interest that are covered in detail include symmetry (and its "spontaneous" breaking), the measurement problem, the Kochen-Specker, Free Will, and Bell Theorems, the Kadison-Singer conjecture, quantization, indistinguishable particles, the quantum theory of large systems, and quantum logic, the latter in connection with the topos approach to quantum theory.

Measurement and Control of Charged Particle Beams

Authors: ---
Book Series: Particle Acceleration and Detection ISBN: 9783642079146 9783540441878 9783662085813 Year: Pages: 364 DOI: 10.1007/978-3-662-08581-3_13 Language: English
Publisher: Springer Nature Grant: Knowledge Unlatched - 104935
Subject: Mathematics
Added to DOAB on : 2019-11-29 11:21:03
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This advanced textbook and reference is the first comprehensive and systematic review of all methods used for the measurement, correction, and control of the beam dynamics of modern particle accelerators. Based on material presented in several lectures at the US Particle Accelerator School, the text is intended for graduate students starting research or work in the field of beam physics. Relativistic beams in linear accelerators and storage rings provide the focus. After a review of linear optics, the text addresses basic and advanced techniques for beam control, plus a variety of methods for the manipulation of particle-beam properties. In each case, specific procedures are illustrated by examples from operational accelerators, e.g., CERN, DESY, SLAC, KEK, LBNL, and FNAL. The book also treats special topics such as injection and extraction methods, beam cooling, spin transport, and polarization. Problems and solutions enhance the book’s usefulness in graduate courses.

Nb3Sn Accelerator Magnets

Authors: ---
Book Series: Particle Acceleration and Detection ISBN: 9783030161187 Year: Pages: 452 DOI: 10.1007/978-3-030-16118-7 Language: English
Publisher: Springer Nature
Subject: Science (General) --- Mathematics --- Agriculture (General)
Added to DOAB on : 2020-01-29 11:21:11
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This open access book is written by world-recognized experts in the fields of applied superconductivity and superconducting accelerator magnet technologies. It provides a contemporary review and assessment of the experience in research and development of high-field accelerator dipole magnets based on Nb3Sn superconductor over the past five decades. The reader attains clear insight into the development and the main properties of Nb3Sn composite superconducting wires and Rutherford cables, and details of accelerator dipole designs, technologies and performance. Special attention is given to innovative features of the developed Nb3Sn magnets. The book concludes with a discussion of accelerator magnet needs for future circular colliders. ; Broadens our understanding of design and performance limits of high-field Nb3Sn accelerator magnets for a future very high energy hadron collider Offers beginners a concise overview of the relevant design concepts for a new generation of superconducting accelerator magnets based on Nb3Sn superconductor Illustrates the complete process of accelerator magnet design and fabrication Provides a contemporary review and assessment of the past experience with Nb3Sn high-field dipole accelerator magnets Identifies the main open R&D issues for Nb3Sn high-field dipole magnets

Principles of Mechanics

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Book Series: Advances in Science, Technology & Innovation ISBN: 9783030151959 Year: Pages: 173 DOI: 10.1007/978-3-030-15195-9 Language: English
Publisher: Springer Nature
Subject: Mathematics --- Agriculture (General)
Added to DOAB on : 2020-02-04 11:21:03
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This open access textbook takes the reader step-by-step through the concepts of mechanics in a clear and detailed manner. Mechanics is considered to be the core of physics, where a deep understanding of the concepts is essential in understanding all branches of physics. Many proofs and examples are included to help the reader grasp the fundamentals fully, paving the way to deal with more advanced topics. After solving all of the examples, the reader will have gained a solid foundation in mechanics and the skills to apply the concepts in a variety of situations. The book is useful for undergraduate students majoring in physics and other science and engineering disciplines. It can also be used as a reference for more advanced levels.

Planar Maps, Random Walks and Circle Packing

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Book Series: Lecture Notes in Mathematics ISBN: 9783030279684 Year: Pages: 120 DOI: 10.1007/978-3-030-27968-4 Language: English
Publisher: Springer Nature
Subject: Mathematics
Added to DOAB on : 2020-01-29 11:21:10
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This open access book focuses on the interplay between random walks on planar maps and Koebe’s circle packing theorem. Further topics covered include electric networks, the He–Schramm theorem on infinite circle packings, uniform spanning trees of planar maps, local limits of finite planar maps and the almost sure recurrence of simple random walks on these limits. One of its main goals is to present a self-contained proof that the uniform infinite planar triangulation (UIPT) is almost surely recurrent. Full proofs of all statements are provided. A planar map is a graph that can be drawn in the plane without crossing edges, together with a specification of the cyclic ordering of the edges incident to each vertex. One widely applicable method of drawing planar graphs is given by Koebe’s circle packing theorem (1936). Various geometric properties of these drawings, such as existence of accumulation points and bounds on the radii, encode important probabilistic information, such as the recurrence/transience of simple random walks and connectivity of the uniform spanning forest. This deep connection is especially fruitful to the study of random planar maps. The book is aimed at researchers and graduate students in mathematics and is suitable for a single-semester course; only a basic knowledge of graduate level probability theory is assumed.

Particle Physics Reference Library

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ISBN: 9783030382070 Year: Pages: 630 DOI: 10.1007/978-3-030-38207-0 Language: English
Publisher: Springer Nature
Subject: Mathematics --- Science (General)
Added to DOAB on : 2020-09-23 00:05:27
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This first open access volume of the handbook series contains articles on the standard model of particle physics, both from the theoretical and experimental perspective. It also covers related topics, such as heavy-ion physics, neutrino physics and searches for new physics beyond the standard model. A joint CERN-Springer initiative, the “Particle Physics Reference Library” provides revised and updated contributions based on previously published material in the well-known Landolt-Boernstein series on particle physics, accelerators and detectors (volumes 21A,B1,B2,C), which took stock of the field approximately one decade ago. Central to this new initiative is publication under full open access.

The Cellular Automaton Interpretation of Quantum Mechanics

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Book Series: Fundamental Theories of Physics ISSN: 0168-1222 ISBN: 9783319412849 9783319412856 Year: Pages: 298 DOI: 10.1007/978-3-319-41285-6 Language: English
Publisher: Springer Nature
Subject: Astronomy (General) --- Geology --- Earth Sciences --- Physics (General)
Added to DOAB on : 2017-02-14 10:09:28
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This book presents the deterministic view of quantum mechanics developed by Nobel Laureate Gerard 't Hooft.Dissatisfied with the uncomfortable gaps in the way conventional quantum mechanics meshes with the classical world, 't Hooft has revived the old hidden variable ideas, but now in a much more systematic way than usual. In this, quantum mechanics is viewed as a tool rather than a theory.The author gives examples of models that are classical in essence, but can be analysed by the use of quantum techniques, and argues that even the Standard Model, together with gravitational interactions, might be viewed as a quantum mechanical approach to analysing a system that could be classical at its core. He shows how this approach, even though it is based on hidden variables, can be plausibly reconciled with Bell's theorem, and how the usual objections voiced against the idea of ‘superdeterminism' can be overcome, at least in principle.This framework elegantly explains - and automatically cures - the problems of the wave function collapse and the measurement problem. Even the existence of an “arrow of time" can perhaps be explained in a more elegant way than usual. As well as reviewing the author’s earlier work in the field, the book also contains many new observations and calculations. It provides stimulating reading for all physicists working on the foundations of quantum theory.

Handbook of Mathematical Geosciences

Authors: --- ---
ISBN: 9783319789996 Year: Pages: 914 DOI: 10.1007/978-3-319-78999-6 Language: English
Publisher: Springer Nature
Subject: Mathematics --- Geology --- Earth Sciences --- Computer Science
Added to DOAB on : 2020-02-05 11:21:16
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This Open Access handbook published at the IAMG's 50th anniversary, presents a compilation of invited path-breaking research contributions by award-winning geoscientists who have been instrumental in shaping the IAMG. It contains 45 chapters that are categorized broadly into five parts (i) theory, (ii) general applications, (iii) exploration and resource estimation, (iv) reviews, and (v) reminiscences covering related topics like mathematical geosciences, mathematical morphology, geostatistics, fractals and multifractals, spatial statistics, multipoint geostatistics, compositional data analysis, informatics, geocomputation, numerical methods, and chaos theory in the geosciences.

Particle Accelerator Physics

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ISBN: 9783319183169 9783319183176 Year: DOI: 10.1007/978-3-319-18317-6 Language: English
Publisher: Springer Nature Grant: Knowledge Unlatched - 104936
Subject: Mathematics
Added to DOAB on : 2019-11-29 11:21:03
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This book by Helmut Wiedemann is a well-established, classic text, providing an in-depth and comprehensive introduction to the field of high-energy particle acceleration and beam dynamics.The present 4th edition has been significantly revised, updated and expanded. The newly conceived Part I is an elementary introduction to the subject matter for undergraduate students. Part II gathers the basic tools in preparation of a more advanced treatment, summarizing the essentials of electrostatics and electrodynamics as well as of particle dynamics in electromagnetic fields. Part III is an extensive primer in beam dynamics, followed, in Part IV, by an introduction and description of the main beam parameters and including a new chapter on beam emittance and lattice design. Part V is devoted to the treatment of perturbations in beam dynamics. Part VI then discusses the details of charged particle acceleration.

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