Mathematics Of Open Quantum Systems The Dissipative And Non Unitary Representations And Quantum Measurements
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Mathematics Of Open Quantum Systems The Dissipative And Non Unitary Representations And Quantum Measurements
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Author : Konstantin A Makarov
language : en
Publisher: World Scientific
Release Date : 2021-12-24
Mathematics Of Open Quantum Systems The Dissipative And Non Unitary Representations And Quantum Measurements written by Konstantin A Makarov and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-12-24 with Science categories.
This book presents new developments in the open quantum systems theory with emphasis on applications to the (frequent) measurement theory.In the first part of the book, the uniqueness theorems for the solutions to the restricted Weyl commutation relations braiding unitary groups and semi-groups of contractions are discussed. The major theme involves an intrinsic characterization of the simplest symmetric operator solutions to the Heisenberg uncertainty relations, the problem posed by Jørgensen and Muhly, followed by the proof of the uniqueness theorems for the simplest solutions to the restricted Weyl commutation relations. The detailed study of unitary invariants of the corresponding dissipative and symmetric operators opens up a look at the classical Stone-von Neumann uniqueness theorem from a new angle and provides an extended version of the uniqueness result relating various realizations of a differentiation operator on the corresponding metric graphs.The second part of the book is devoted to mathematical problems of the quantum measurements under continuous monitoring. Among the topics discussed are the complementarity of the Quantum Zeno effect and Exponential Decay scenario in frequent quantum measurements, and a rigorous treatment, within continuous monitoring paradigm, of the celebrated 'double-slit experiment' where the renowned exclusive and interference measurement alternatives approach in quantum theory is presented in a way that is accessible for mathematicians. One of the striking applications of the generalized (1-stable) central limit theorem is the mathematical evidence of exponential decay of unstable states of the quantum pendulum under continuous monitoring.
A Mathematical Introduction To Electronic Structure Theory
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Author : Lin Lin
language : en
Publisher: SIAM
Release Date : 2019-06-05
A Mathematical Introduction To Electronic Structure Theory written by Lin Lin and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-06-05 with Mathematics categories.
Based on first principle quantum mechanics, electronic structure theory is widely used in physics, chemistry, materials science, and related fields and has recently received increasing research attention in applied and computational mathematics. This book provides a self-contained, mathematically oriented introduction to the subject and its associated algorithms and analysis. It will help applied mathematics students and researchers with minimal background in physics understand the basics of electronic structure theory and prepare them to conduct research in this area. The book begins with an elementary introduction of quantum mechanics, including the uncertainty principle and the Hartree?Fock theory, which is considered the starting point of modern electronic structure theory. The authors then provide an in-depth discussion of two carefully selected topics that are directly related to several aspects of modern electronic structure calculations: density matrix based algorithms and linear response theory. Chapter 2 introduces the Kohn?Sham density functional theory with a focus on the density matrix based numerical algorithms, and Chapter 3 introduces linear response theory, which provides a unified viewpoint of several important phenomena in physics and numerics. An understanding of these topics will prepare readers for more advanced topics in this field. The book concludes with the random phase approximation to the correlation energy. The book is written for advanced undergraduate and beginning graduate students, specifically those with mathematical backgrounds but without a priori knowledge of quantum mechanics, and can be used for self-study by researchers, instructors, and other scientists. The book can also serve as a starting point to learn about many-body perturbation theory, a topic at the frontier of the study of interacting electrons.
Open Quantum Systems
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Author : Ángel Rivas
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-10-01
Open Quantum Systems written by Ángel Rivas 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 2011-10-01 with Science categories.
In this volume the fundamental theory of open quantum systems is revised in the light of modern developments in the field. A unified approach to the quantum evolution of open systems is presented by merging concepts and methods traditionally employed by different communities, such as quantum optics, condensed matter, chemical physics and mathematical physics. The mathematical structure and the general properties of the dynamical maps underlying open system dynamics are explained in detail. The microscopic derivation of dynamical equations, including both Markovian and non-Markovian evolutions, is also discussed. Because of the step-by-step explanations, this work is a useful reference to novices in this field. However, experienced researches can also benefit from the presentation of recent results.
Open Quantum Systems I
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Author : Stéphane Attal
language : en
Publisher: Springer
Release Date : 2006-08-18
Open Quantum Systems I written by Stéphane Attal and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-08-18 with Mathematics categories.
Understanding dissipative dynamics of open quantum systems remains a challenge in mathematical physics. This problem is relevant in various areas of fundamental and applied physics. Significant progress in the understanding of such systems has been made recently. These books present the mathematical theories involved in the modeling of such phenomena. They describe physically relevant models, develop their mathematical analysis and derive their physical implications.
Open Quantum Systems Iii
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Author : Stéphane Attal
language : en
Publisher: Springer
Release Date : 2006-08-18
Open Quantum Systems Iii written by Stéphane Attal and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-08-18 with Mathematics categories.
This volume is the third and last of a series devoted to the lecture notes of the Grenoble Summer School on “Open Quantum Systems” which took place at the th th Institut Fourier from June 16 to July 4 2003. The contributions presented in this volumecorrespondtoexpanded versionsofthelecturenotesprovidedbytheauthors to the students of the Summer School. The corresponding lectures were scheduled in the last part of the School devoted to recent developments in the study of Open Quantum Systems. Whereas the rst two volumes were dedicated to a detailed exposition of the mathematical techniques and physical concepts relevant in the study of Open S- tems with noapriori pre-requisites, the contributions presented in this volume request from the reader some familiarity with these aspects. Indeed, the material presented here aims at leading the reader already acquainted with the basics in ? quantum statistical mechanics, spectral theory of linear operators,C -dynamical systems, and quantum stochastic differential equations to the front of the current research done on various aspects of Open Quantum Systems. Nevertheless, pe- gogical efforts have been made by the various authors of these notes so that this volume should be essentially self-contained for a reader with minimal previous - posure to the themes listed above. In any case, the reader in need of complements can always turn to these rst two volumes. The topics covered in these lectures notes start with an introduction to n- equilibrium quantum statistical mechanics.
Quantum Dissipative Systems
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Author : Ulrich Weiss
language : en
Publisher: World Scientific
Release Date : 2012
Quantum Dissipative Systems written by Ulrich Weiss and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012 with Mathematics categories.
Starting from first principles, this book introduces the fundamental concepts and methods of dissipative quantum mechanics and explores related phenomena in condensed matter systems. Major experimental achievements in cooperation with theoretical advances have brightened the field and brought it to the attention of the general community in natural sciences. Nowadays, working knowledge of dissipative quantum mechanics is an essential tool for many physicists. This book -- originally published in 1990 and republished in 1999 and and 2008 as enlarged second and third editions -- delves significantly deeper than ever before into the fundamental concepts, methods and applications of quantum dissipative systems.This fourth edition provides a self-contained and updated account of the quantum mechanics of open systems and offers important new material including the most recent developments. The subject matter has been expanded by about fifteen percent. Many chapters have been completely rewritten to better cater to both the needs of newcomers to the field and the requests of the advanced readership. Two chapters have been added that account for recent progress in the field. This book should be accessible to all graduate students in physics. Researchers will find this a rich and stimulating source.
Physics Briefs
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Author :
language : en
Publisher:
Release Date : 1994
Physics Briefs written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994 with Physics categories.
Mathematical Reviews
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Author :
language : en
Publisher:
Release Date : 2005
Mathematical Reviews written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with Mathematics categories.
Mathematical Foundations Of Quantum Theory
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Author : A. R. Marlow
language : en
Publisher:
Release Date : 1978
Mathematical Foundations Of Quantum Theory written by A. R. Marlow and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1978 with Science categories.
Mathematical Foundations of Quantum Theory is a collection of papers presented at the 1977 conference on the Mathematical Foundations of Quantum Theory, held in New Orleans. The contributors present their topics from a wide variety of backgrounds and specialization, but all shared a common interest in answering quantum issues. Organized into 20 chapters, this book's opening chapters establish a sound mathematical basis for quantum theory and a mode of observation in the double slit experiment. This book then describes the Lorentz particle system and other mathematical structures with which fun ...
Open Quantum Systems Ii
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Author : Stéphane Attal
language : en
Publisher: Springer
Release Date : 2006-08-29
Open Quantum Systems Ii written by Stéphane Attal and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-08-29 with Mathematics categories.
Understanding dissipative dynamics of open quantum systems remains a challenge in mathematical physics. This problem is relevant in various areas of fundamental and applied physics. Significant progress in the understanding of such systems has been made recently. These books present the mathematical theories involved in the modeling of such phenomena. They describe physically relevant models, develop their mathematical analysis and derive their physical implications.