Introduction To Tensor Network Methods

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Introduction To Tensor Network Methods

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Author : Simone Montangero
language : en
Publisher: Springer
Release Date : 2018-12-02

Introduction To Tensor Network Methods written by Simone Montangero and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-12-02 with Science categories.

This volume of lecture notes briefly introduces the basic concepts needed in any computational physics course: software and hardware, programming skills, linear algebra, and differential calculus. It then presents more advanced numerical methods to tackle the quantum many-body problem: it reviews the numerical renormalization group and then focuses on tensor network methods, from basic concepts to gauge invariant ones. Finally, in the last part, the author presents some applications of tensor network methods to equilibrium and out-of-equilibrium correlated quantum matter. The book can be used for a graduate computational physics course. After successfully completing such a course, a student should be able to write a tensor network program and can begin to explore the physics of many-body quantum systems. The book can also serve as a reference for researchers working or starting out in the field.

Introduction To Tensor Network Methods

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Author : Simone Montangero
language : en
Publisher: Springer
Release Date : 2018-11-28

Introduction To Tensor Network Methods written by Simone Montangero and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-11-28 with Science categories.

This volume of lecture notes briefly introduces the basic concepts needed in any computational physics course: software and hardware, programming skills, linear algebra, and differential calculus. It then presents more advanced numerical methods to tackle the quantum many-body problem: it reviews the numerical renormalization group and then focuses on tensor network methods, from basic concepts to gauge invariant ones. Finally, in the last part, the author presents some applications of tensor network methods to equilibrium and out-of-equilibrium correlated quantum matter. The book can be used for a graduate computational physics course. After successfully completing such a course, a student should be able to write a tensor network program and can begin to explore the physics of many-body quantum systems. The book can also serve as a reference for researchers working or starting out in the field.

Tensor Network Contractions

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Author : Shi-Ju Ran
language : en
Publisher: Springer Nature
Release Date : 2020-01-27

Tensor Network Contractions written by Shi-Ju Ran and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-01-27 with Science categories.

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.

Density Matrix And Tensor Network Renormalization

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Author : Tao Xiang
language : en
Publisher: Cambridge University Press
Release Date : 2023-08-31

Density Matrix And Tensor Network Renormalization written by Tao Xiang 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 2023-08-31 with Science categories.

Renormalization group theory of tensor network states provides a powerful tool for studying quantum many-body problems and a new paradigm for understanding entangled structures of complex systems. In recent decades the theory has rapidly evolved into a universal framework and language employed by researchers in fields ranging from condensed matter theory to machine learning. This book presents a pedagogical and comprehensive introduction to this field for the first time. After an introductory survey on the major advances in tensor network algorithms and their applications, it introduces step-by-step the tensor network representations of quantum states and the tensor-network renormalization group methods developed over the past three decades. Basic statistical and condensed matter physics models are used to demonstrate how the tensor network renormalization works. An accessible primer for scientists and engineers, this book would also be ideal as a reference text for a graduate course in this area.

High Performance Tensor Computations In Scientific Computing And Data Science

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Author : Edoardo Angelo Di Napoli
language : en
Publisher: Frontiers Media SA
Release Date : 2022-11-08

High Performance Tensor Computations In Scientific Computing And Data Science written by Edoardo Angelo Di Napoli and has been published by Frontiers Media SA this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-11-08 with Science categories.

On Exciton Vibration And Exciton Photon Interactions In Organic Semiconductors

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Author : Antonios M. Alvertis
language : en
Publisher: Springer Nature
Release Date : 2021-10-25

On Exciton Vibration And Exciton Photon Interactions In Organic Semiconductors written by Antonios M. Alvertis and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-10-25 with Science categories.

What are the physical mechanisms that underlie the efficient generation and transfer of energy at the nanoscale? Nature seems to know the answer to this question, having optimised the process of photosynthesis in plants over millions of years of evolution. It is conceivable that humans could mimic this process using synthetic materials, and organic semiconductors have attracted a lot of attention in this respect. Once an organic semiconductor absorbs light, bound pairs of electrons with positively charged holes, termed `excitons’, are formed. Excitons behave as fundamental energy carriers, hence understanding the physics behind their efficient generation and transfer is critical to realising the potential of organic semiconductors for light-harvesting and other applications, such as LEDs and transistors. However, this problem is extremely challenging since excitons can interact very strongly with photons. Moreover, simultaneously with the exciton motion, organic molecules can vibrate in hundreds of possible ways, having a very strong effect on energy transfer. The description of these complex phenomena is often beyond the reach of standard quantum mechanical methods which rely on the assumption of weak interactions between excitons, photons and vibrations. In this thesis, Antonios Alvertis addresses this problem through the development and application of a variety of different theoretical methods to the description of these strong interactions, providing pedagogical explanations of the underlying physics. A comprehensive introduction to organic semiconductors is followed by a review of the background theory that is employed to approach the relevant research questions, and the theoretical results are presented in close connection with experiment, yielding valuable insights for experimentalists and theoreticians alike.

Introduction To Many Body Physics

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Author : Piers Coleman
language : en
Publisher: Cambridge University Press
Release Date : 2015-11-26

Introduction To Many Body Physics written by Piers Coleman 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 2015-11-26 with Science categories.

This book explains the tools and concepts needed for a research-level understanding of the subject, for graduate students in condensed matter physics.

Signal Processing And Machine Learning Theory

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Author : Paulo S.R. Diniz
language : en
Publisher: Elsevier
Release Date : 2023-07-10

Signal Processing And Machine Learning Theory written by Paulo S.R. Diniz and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-07-10 with Technology & Engineering categories.

Signal Processing and Machine Learning Theory, authored by world-leading experts, reviews the principles, methods and techniques of essential and advanced signal processing theory. These theories and tools are the driving engines of many current and emerging research topics and technologies, such as machine learning, autonomous vehicles, the internet of things, future wireless communications, medical imaging, etc. - Provides quick tutorial reviews of important and emerging topics of research in signal processing-based tools - Presents core principles in signal processing theory and shows their applications - Discusses some emerging signal processing tools applied in machine learning methods - References content on core principles, technologies, algorithms and applications - Includes references to journal articles and other literature on which to build further, more specific, and detailed knowledge

Emergent Phenomena In Correlated Matter

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Author : Eva Pavarini
language : en
Publisher: Forschungszentrum Jülich
Release Date : 2013

Emergent Phenomena In Correlated Matter written by Eva Pavarini and has been published by Forschungszentrum Jülich this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013 with categories.

Mathematics Of Autonomy Mathematical Methods For Cyber Physical Cognitive Systems

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Author : Vladimir G Ivancevic
language : en
Publisher: World Scientific
Release Date : 2017-10-30

Mathematics Of Autonomy Mathematical Methods For Cyber Physical Cognitive Systems written by Vladimir G Ivancevic and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-10-30 with Computers categories.

Mathematics of Autonomy provides solid mathematical foundations for building useful Autonomous Systems. It clarifies what makes a system autonomous rather than simply automated, and reveals the inherent limitations of systems currently incorrectly labeled as autonomous in reference to the specific and strong uncertainty that characterizes the environments they operate in. Such complex real-world environments demand truly autonomous solutions to provide the flexibility and robustness needed to operate well within them.This volume embraces hybrid solutions to demonstrate extending the classes of uncertainty autonomous systems can handle. In particular, it combines physical-autonomy (robots), cyber-autonomy (agents) and cognitive-autonomy (cyber and embodied cognition) to produce a rigorous subset of trusted autonomy: Cyber-Physical-Cognitive autonomy (CPC-autonomy).The body of the book alternates between underlying theory and applications of CPC-autonomy including 'Autonomous Supervision of a Swarm of Robots' , 'Using Wind Turbulence against a Swarm of UAVs' and 'Unique Super-Dynamics for All Kinds of Robots (UAVs, UGVs, UUVs and USVs)' to illustrate how to effectively construct Autonomous Systems using this model. It avoids the wishful thinking that characterizes much discussion related to autonomy, discussing the hard limits and challenges of real autonomous systems. In so doing, it clarifies where more work is needed, and also provides a rigorous set of tools to tackle some of the problem space.