The Mathematical Aspects Of Quantum Maps
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The Mathematical Aspects Of Quantum Maps
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Author : Mirko Esposti
language : en
Publisher: Springer Science & Business Media
Release Date : 2003-06-04
The Mathematical Aspects Of Quantum Maps written by Mirko Esposti 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 2003-06-04 with Science categories.
Quantum maps are presented with special emphasis on their physical origin. They represent a testing ground for understanding concepts in quantized chaotic systems. The book teaches the modern mathematical methods from analytic and algebraic number theory as applied to quantum maps. It gives a broad and in-depth overview of the mathematical problems arising in this area. Also treated are the numerical aspects in quantum chaos such as eigenvalue and eigenfunctions computations for chaotic quantum systems. The book addresses scientists and advanced students in mathematics and mathematical physics.
The Mathematical Aspects Of Quantum Maps
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Author : Mirko Esposti
language : en
Publisher: Springer
Release Date : 2014-03-12
The Mathematical Aspects Of Quantum Maps written by Mirko Esposti and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-03-12 with Science categories.
Quantum maps are presented with special emphasis on their physical origin. They represent a testing ground for understanding concepts in quantized chaotic systems. The book teaches the modern mathematical methods from analytic and algebraic number theory as applied to quantum maps. It gives a broad and in-depth overview of the mathematical problems arising in this area. Also treated are the numerical aspects in quantum chaos such as eigenvalue and eigenfunctions computations for chaotic quantum systems. The book addresses scientists and advanced students in mathematics and mathematical physics.
The Mathematical Aspects Of Quantum Maps
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Author : Mirko Esposti
language : en
Publisher: Springer
Release Date : 2008-01-11
The Mathematical Aspects Of Quantum Maps written by Mirko Esposti and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-01-11 with Science categories.
Quantum maps are presented with special emphasis on their physical origin. They represent a testing ground for understanding concepts in quantized chaotic systems. The book teaches the modern mathematical methods from analytic and algebraic number theory as applied to quantum maps. It gives a broad and in-depth overview of the mathematical problems arising in this area. Also treated are the numerical aspects in quantum chaos such as eigenvalue and eigenfunctions computations for chaotic quantum systems. The book addresses scientists and advanced students in mathematics and mathematical physics.
Mathematical Aspects Of Quantum Field Theories
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Author : Damien Calaque
language : en
Publisher: Springer
Release Date : 2015-01-06
Mathematical Aspects Of Quantum Field Theories written by Damien Calaque and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-01-06 with Science categories.
Despite its long history and stunning experimental successes, the mathematical foundation of perturbative quantum field theory is still a subject of ongoing research. This book aims at presenting some of the most recent advances in the field, and at reflecting the diversity of approaches and tools invented and currently employed. Both leading experts and comparative newcomers to the field present their latest findings, helping readers to gain a better understanding of not only quantum but also classical field theories. Though the book offers a valuable resource for mathematicians and physicists alike, the focus is more on mathematical developments. This volume consists of four parts: The first Part covers local aspects of perturbative quantum field theory, with an emphasis on the axiomatization of the algebra behind the operator product expansion. The second Part highlights Chern-Simons gauge theories, while the third examines (semi-)classical field theories. In closing, Part 4 addresses factorization homology and factorization algebras.
Dynamics Information And Complexity In Quantum Systems
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Author : Fabio Benatti
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-04-17
Dynamics Information And Complexity In Quantum Systems written by Fabio Benatti 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 2009-04-17 with Computers categories.
This book offers a self-contained overview of the entropic approach to quantum dynamical systems. In it, complexity in quantum dynamics is addressed by comparison with the classical ergodic, information, and algorithmic complexity theories.
Quantum Machine Learning
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Author : Claudio Conti
language : en
Publisher: Springer Nature
Release Date : 2023-12-27
Quantum Machine Learning written by Claudio Conti and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-12-27 with Science categories.
This book presents a new way of thinking about quantum mechanics and machine learning by merging the two. Quantum mechanics and machine learning may seem theoretically disparate, but their link becomes clear through the density matrix operator which can be readily approximated by neural network models, permitting a formulation of quantum physics in which physical observables can be computed via neural networks. As well as demonstrating the natural affinity of quantum physics and machine learning, this viewpoint opens rich possibilities in terms of computation, efficient hardware, and scalability. One can also obtain trainable models to optimize applications and fine-tune theories, such as approximation of the ground state in many body systems, and boosting quantum circuits’ performance. The book begins with the introduction of programming tools and basic concepts of machine learning, with necessary background material from quantum mechanics and quantum information also provided. This enables the basic building blocks, neural network models for vacuum states, to be introduced. The highlights that follow include: non-classical state representations, with squeezers and beam splitters used to implement the primary layers for quantum computing; boson sampling with neural network models; an overview of available quantum computing platforms, their models, and their programming; and neural network models as a variational ansatz for many-body Hamiltonian ground states with applications to Ising machines and solitons. The book emphasizes coding, with many open source examples in Python and TensorFlow, while MATLAB and Mathematica routines clarify and validate proofs. This book is essential reading for graduate students and researchers who want to develop both the requisite physics and coding knowledge to understand the rich interplay of quantum mechanics and machine learning.
Spectral Theory And Applications
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Author : Alexandre Girouard
language : en
Publisher: American Mathematical Soc.
Release Date : 2018-11-21
Spectral Theory And Applications written by Alexandre Girouard and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-11-21 with Mathematics categories.
This book is a collection of lecture notes and survey papers based on the minicourses given by leading experts at the 2016 CRM Summer School on Spectral Theory and Applications, held from July 4–14, 2016, at Université Laval, Québec City, Québec, Canada. The papers contained in the volume cover a broad variety of topics in spectral theory, starting from the fundamentals and highlighting its connections to PDEs, geometry, physics, and numerical analysis.
Quantum Gravity
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Author : Domenico J. W. Giulini
language : en
Publisher: Springer Science & Business Media
Release Date : 2003-09-16
Quantum Gravity written by Domenico J. W. Giulini 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 2003-09-16 with Science categories.
The relation between quantum theory and the theory of gravitation remains one of the most outstanding unresolved issues of modern physics. According to general expectation, general relativity as well as quantum (field) theory in a fixed background spacetime cannot be fundamentally correct. Hence there should exist a broader theory comprising both in appropriate limits, i.e., quantum gravity. This book gives readers a comprehensive introduction accessible to interested non-experts to the main issues surrounding the search for quantum gravity. These issues relate to fundamental questions concerning the various formalisms of quantization; specific questions concerning concrete processes, like gravitational collapse or black-hole evaporation; and the all important question concerning the possibility of experimental tests of quantum-gravity effects.
Stochastic Processes And Random Matrices
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Author : Grégory Schehr
language : en
Publisher: Oxford University Press
Release Date : 2017-08-15
Stochastic Processes And Random Matrices written by Grégory Schehr and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-08-15 with Science categories.
The field of stochastic processes and Random Matrix Theory (RMT) has been a rapidly evolving subject during the last fifteen years. The continuous development and discovery of new tools, connections and ideas have led to an avalanche of new results. These breakthroughs have been made possible thanks, to a large extent, to the recent development of various new techniques in RMT. Matrix models have been playing an important role in theoretical physics for a long time and they are currently also a very active domain of research in mathematics. An emblematic example of these recent advances concerns the theory of growth phenomena in the Kardar-Parisi-Zhang (KPZ) universality class where the joint efforts of physicists and mathematicians during the last twenty years have unveiled the beautiful connections between this fundamental problem of statistical mechanics and the theory of random matrices, namely the fluctuations of the largest eigenvalue of certain ensembles of random matrices. This text not only covers this topic in detail but also presents more recent developments that have emerged from these discoveries, for instance in the context of low dimensional heat transport (on the physics side) or integrable probability (on the mathematical side).
Granular Gas Dynamics
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Author : Thorsten Pöschel
language : en
Publisher: Springer Science & Business Media
Release Date : 2003-10-16
Granular Gas Dynamics written by Thorsten Pöschel 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 2003-10-16 with Science categories.
The contributions in this book address both the kinetic approach one using the Boltzmann equation for dissipative gases as well as the less established hydrodynamic description. The last part of the book is devoted to driven granular gases and their analogy with molecular fluids.