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Modelling Non-Markovian Quantum Systems Using Tensor Networks

2020-08-31 Science
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Release : 2020-08-31
Genre : Science
Kind : eBook
Book Rating : 755/5 ( reviews)

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Book Synopsis Modelling Non-Markovian Quantum Systems Using Tensor Networks by : Aidan Strathearn

Download or read book Modelling Non-Markovian Quantum Systems Using Tensor Networks written by Aidan Strathearn. This book was released on 2020-08-31. Available in PDF, EPUB and Kindle. Book excerpt: This thesis presents a revolutionary technique for modelling the dynamics of a quantum system that is strongly coupled to its immediate environment. This is a challenging but timely problem. In particular it is relevant for modelling decoherence in devices such as quantum information processors, and how quantum information moves between spatially separated parts of a quantum system. The key feature of this work is a novel way to represent the dynamics of general open quantum systems as tensor networks, a result which has connections with the Feynman operator calculus and process tensor approaches to quantum mechanics. The tensor network methodology developed here has proven to be extremely powerful: For many situations it may be the most efficient way of calculating open quantum dynamics. This work is abounds with new ideas and invention, and is likely to have a very significant impact on future generations of physicists.

Process Tensor Networks for Non-Markovian Open Quantum Systems

2022 Many-body problem
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Release : 2022
Genre : Many-body problem
Kind : eBook
Book Rating : /5 ( reviews)

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Book Synopsis Process Tensor Networks for Non-Markovian Open Quantum Systems by : Gerald E. Fux

Download or read book Process Tensor Networks for Non-Markovian Open Quantum Systems written by Gerald E. Fux. This book was released on 2022. Available in PDF, EPUB and Kindle. Book excerpt:

Tensor Network Contractions

2020-01-27 Science
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Release : 2020-01-27
Genre : Science
Kind : eBook
Book Rating : 894/5 ( reviews)

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Book Synopsis Tensor Network Contractions by : Shi-Ju Ran

Download or read book Tensor Network Contractions written by Shi-Ju Ran. This book was released on 2020-01-27. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Introduction to Tensor Network Methods

2018-11-28 Science
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Release : 2018-11-28
Genre : Science
Kind : eBook
Book Rating : 096/5 ( reviews)

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Book Synopsis Introduction to Tensor Network Methods by : Simone Montangero

Download or read book Introduction to Tensor Network Methods written by Simone Montangero. This book was released on 2018-11-28. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Simulation with Entropy Thermodynamics

2021-03-11 Science
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Release : 2021-03-11
Genre : Science
Kind : eBook
Book Rating : 142/5 ( reviews)

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Book Synopsis Simulation with Entropy Thermodynamics by : Christophe Goupil

Download or read book Simulation with Entropy Thermodynamics written by Christophe Goupil. This book was released on 2021-03-11. Available in PDF, EPUB and Kindle. Book excerpt: Beyond its identification with the second law of thermodynamics, entropy is a formidable tool for describing systems in their relationship with their environment. This book proposes to go through some of these situations where the formulation of entropy, and more precisely, the production of entropy in out-of-equilibrium processes, makes it possible to forge an approach to the behavior of very different systems. Whether for dimensioning structures; influencing parameter variability; or optimizing power, efficiency, or waste heat reduction, simulations based on entropy production offer a tool that is both compact and reliable. In the case of systems marked by complexity, it appears to be the only way. In that sense, realistic optimization can be carried out, integrating within the same framework both the system and all the constraints and boundary conditions that define it. Simulations based on entropy give the researcher a powerful analytical framework that crosses the disciplines of physics and links them together.

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