Quantum Quadratic Operators and Processes
Quantum Quadratic Operators and Processes

Author: Farrukh Mukhamedov

Publisher: Springer

Published: 2015-10-12

Total Pages: 243

ISBN-13: 3319228374

DOWNLOAD EBOOK

Covering both classical and quantum approaches, this unique and self-contained book presents the most recent developments in the theory of quadratic stochastic operators and their Markov and related processes. The asymptotic behavior of dynamical systems generated by classical and quantum quadratic operators is investigated and various properties of quantum quadratic operators are studied, providing an insight into the construction of quantum channels. This book is suitable as a textbook for an advanced undergraduate/graduate level course or summer school in quantum dynamical systems. It can also be used as a reference book by researchers looking for interesting problems to work on, or useful techniques and discussions of particular problems. Since it includes the latest developments in the fields of quadratic dynamical systems, Markov processes and quantum stochastic processes, researchers at all levels are likely to find the book inspiring and useful.

On Kadison's Schwarz Inequality for Quantum Quadratic Operators on M2(C) and Their Dynamics
On Kadison's Schwarz Inequality for Quantum Quadratic Operators on M2(C) and Their Dynamics

Author: Abduaziz Abduganiev

Publisher:

Published: 2011

Total Pages: 166

ISBN-13:

DOWNLOAD EBOOK

In this thesis we describe bistochastic Kadison-Schwarz operators on M2(C). Such a description allows us to find positive, but not Kadison-Schwarz operators. Moreover, by means of such a characterization we construct Kadison-Schwarz operators, which are not completely positive. Then we describe quantum quadratic operators on M2(C) with Haar state. Using such a description, we find a necessary condition for quantum quadratic operators that satisfy the Kadison-Schwarz property. This condition allows us to construct quantum quadratic operators which are not Kadison-Schwarz ones. Also we provide examples of quadratic operators for which corresponding linear mappings are not positive. Furthermore, we study nonlinear dynamics of quadratic operators acting the set of states of M2(C). Namely, we find some conditions for the stability of unique fixed point of such operators. Besides, dynamics of certain concrete quadratic operators are investigated.

Infinite Dimensional Analysis, Quantum Probability and Applications
Infinite Dimensional Analysis, Quantum Probability and Applications

Author: Luigi Accardi

Publisher: Springer Nature

Published: 2022-10-04

Total Pages: 369

ISBN-13: 3031061705

DOWNLOAD EBOOK

This proceedings volume gathers selected, peer-reviewed papers presented at the 41st International Conference on Infinite Dimensional Analysis, Quantum Probability and Related Topics (QP41) that was virtually held at the United Arab Emirates University (UAEU) in Al Ain, Abu Dhabi, from March 28th to April 1st, 2021. The works cover recent developments in quantum probability and infinite dimensional analysis, with a special focus on applications to mathematical physics and quantum information theory. Covered topics include white noise theory, quantum field theory, quantum Markov processes, free probability, interacting Fock spaces, and more. By emphasizing the interconnection and interdependence of such research topics and their real-life applications, this reputed conference has set itself as a distinguished forum to communicate and discuss new findings in truly relevant aspects of theoretical and applied mathematics, notably in the field of mathematical physics, as well as an event of choice for the promotion of mathematical applications that address the most relevant problems found in industry. That makes this volume a suitable reading not only for researchers and graduate students with an interest in the field but for practitioners as well.

Quantum Optomechanics
Quantum Optomechanics

Author: Warwick P. Bowen

Publisher: CRC Press

Published: 2015-11-18

Total Pages: 375

ISBN-13: 1482259168

DOWNLOAD EBOOK

Written by leading experimentalist Warwick P. Bowen and prominent theoretician Gerard J. Milburn, Quantum Optomechanics discusses modern developments in this novel field from experimental and theoretical standpoints. The authors share their insight on a range of important topics, including optomechanical cooling and entanglement; quantum limits on

Non-Selfadjoint Operators in Quantum Physics
Non-Selfadjoint Operators in Quantum Physics

Author: Fabio Bagarello

Publisher: John Wiley & Sons

Published: 2015-07-24

Total Pages: 434

ISBN-13: 1118855264

DOWNLOAD EBOOK

A unique discussion of mathematical methods with applications to quantum mechanics Non-Selfadjoint Operators in Quantum Physics: Mathematical Aspects presents various mathematical constructions influenced by quantum mechanics and emphasizes the spectral theory of non-adjoint operators. Featuring coverage of functional analysis and algebraic methods in contemporary quantum physics, the book discusses the recent emergence of unboundedness of metric operators, which is a serious issue in the study of parity-time-symmetric quantum mechanics. The book also answers mathematical questions that are currently the subject of rigorous analysis with potentially significant physical consequences. In addition to prompting a discussion on the role of mathematical methods in the contemporary development of quantum physics, the book features: Chapter contributions written by well-known mathematical physicists who clarify numerous misunderstandings and misnomers while shedding light on new approaches in this growing area An overview of recent inventions and advances in understanding functional analytic and algebraic methods for non-selfadjoint operators as well as the use of Krein space theory and perturbation theory Rigorous support of the progress in theoretical physics of non-Hermitian systems in addition to mathematically justified applications in various domains of physics such as nuclear and particle physics and condensed matter physics An ideal reference, Non-Selfadjoint Operators in Quantum Physics: Mathematical Aspects is useful for researchers, professionals, and academics in applied mathematics and theoretical and/or applied physics who would like to expand their knowledge of classical applications of quantum tools to address problems in their research. Also a useful resource for recent and related trends, the book is appropriate as a graduate-level and/or PhD-level text for courses on quantum mechanics and mathematical models in physics.

Operator Methods in Quantum Mechanics
Operator Methods in Quantum Mechanics

Author: Martin Schechter

Publisher: Elsevier

Published: 2012-12-02

Total Pages: 347

ISBN-13: 0444601058

DOWNLOAD EBOOK

Operator Methods in Quantum Mechanics demonstrates the power of operator theory as a tool in the study of quantum mechanics. More specifically, it shows how to use algebraic, representation-independent methods to solve one- and three-dimensional problems, including certain relativistic problems. It explains the applications of commutation relations, shift operators, and the virial, hypervirial, and Hellman-Feyman theorems to the calculation of eigenvalues, matrix elements, and wave functions. Organized into 16 chapters, this book begins by presenting a few simple postulates describing quantum theory and looking at a single particle moving along a straight line. Then, it introduces mathematical techniques that answer questions about the particle. It also discusses the use of spectral theorem in answering various questions concerning observables, along with negative eigenvalues and methods of determining parts of the spectrum or estimating lower bounds. Moreover, it explains the time-independent or stationary-state scattering theory and states, long-range potentials, and completeness and strong completeness. Oscillating potentials, eigenfunction expansions, restricted particles, hard-core potentials, the invariance principle, and the use of trace class operators to treat scattering theory are also described in this book. This volume is a valuable resource for physicists, as well as students of intermediate quantum mechanics and postgraduate students who want to be acquainted with the algebraic method of solving quantum mechanical problems.

White Noise Analysis And Quantum Information
White Noise Analysis And Quantum Information

Author: Luigi Accardi

Publisher: World Scientific

Published: 2017-08-29

Total Pages: 243

ISBN-13: 9813225475

DOWNLOAD EBOOK

This volume is to pique the interest of many researchers in the fields of infinite dimensional analysis and quantum probability. These fields have undergone increasingly significant developments and have found many new applications, in particular, to classical probability and to different branches of physics. These fields are rather wide and are of a strongly interdisciplinary nature. For such a purpose, we strove to bridge among these interdisciplinary fields in our Workshop on IDAQP and their Applications that was held at the Institute for Mathematical Sciences, National University of Singapore from 3-7 March 2014. Readers will find that this volume contains all the exciting contributions by well-known researchers in search of new directions in these fields.

The Control Handbook
The Control Handbook

Author: William S. Levine

Publisher: CRC Press

Published: 2018-10-08

Total Pages: 944

ISBN-13: 1420073613

DOWNLOAD EBOOK

At publication, The Control Handbook immediately became the definitive resource that engineers working with modern control systems required. Among its many accolades, that first edition was cited by the AAP as the Best Engineering Handbook of 1996. Now, 15 years later, William Levine has once again compiled the most comprehensive and authoritative resource on control engineering. He has fully reorganized the text to reflect the technical advances achieved since the last edition and has expanded its contents to include the multidisciplinary perspective that is making control engineering a critical component in so many fields. Now expanded from one to three volumes, The Control Handbook, Second Edition organizes cutting-edge contributions from more than 200 leading experts. The second volume, Control System Applications, includes 35 entirely new applications organized by subject area. Covering the design and use of control systems, this volume includes applications for: Automobiles, including PEM fuel cells Aerospace Industrial control of machines and processes Biomedical uses, including robotic surgery and drug discovery and development Electronics and communication networks Other applications are included in a section that reflects the multidisciplinary nature of control system work. These include applications for the construction of financial portfolios, earthquake response control for civil structures, quantum estimation and control, and the modeling and control of air conditioning and refrigeration systems. As with the first edition, the new edition not only stands as a record of accomplishment in control engineering but provides researchers with the means to make further advances. Progressively organized, the other two volumes in the set include: Control System Fundamentals Control System Advanced Methods

Emergence Of The Quantum From The Classical: Mathematical Aspects Of Quantum Processes
Emergence Of The Quantum From The Classical: Mathematical Aspects Of Quantum Processes

Author: Maurice A De Gosson

Publisher: World Scientific

Published: 2017-11-10

Total Pages: 306

ISBN-13: 1786344165

DOWNLOAD EBOOK

The emergence of quantum mechanics from classical world mechanics is now a well-established theme in mathematical physics. This book demonstrates that quantum mechanics can indeed be viewed as a refinement of Hamiltonian mechanics, and builds on the work of George Mackey in relation to their mathematical foundations. Additionally when looking at the differences with classical mechanics, quantum mechanics crucially depends on the value of Planck's constant h. Recent cosmological observations tend to indicate that not only the fine structure constant α but also h might have varied in both time and space since the Big Bang. We explore the mathematical and physical consequences of a variation of h; surprisingly we see that a decrease of h leads to transitions from the quantum to the classical.Emergence of the Quantum from the Classical provides help to undergraduate and graduate students of mathematics, physics and quantum theory looking to advance into research in the field.