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Author: Alberto Barchielli
Publisher: Springer Science & Business Media
ISBN: 3642012973
Category : Mathematics
Languages : en
Pages : 331
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Book Description
This course-based monograph introduces the reader to the theory of continuous measurements in quantum mechanics and provides some benchmark applications. The approach chosen, quantum trajectory theory, is based on the stochastic Schrödinger and master equations, which determine the evolution of the a-posteriori state of a continuously observed quantum system and give the distribution of the measurement output. The present introduction is restricted to finite-dimensional quantum systems and diffusive outputs. Two appendices introduce the tools of probability theory and quantum measurement theory which are needed for the theoretical developments in the first part of the book. First, the basic equations of quantum trajectory theory are introduced, with all their mathematical properties, starting from the existence and uniqueness of their solutions. This makes the text also suitable for other applications of the same stochastic differential equations in different fields such as simulations of master equations or dynamical reduction theories. In the next step the equivalence between the stochastic approach and the theory of continuous measurements is demonstrated. To conclude the theoretical exposition, the properties of the output of the continuous measurement are analyzed in detail. This is a stochastic process with its own distribution, and the reader will learn how to compute physical quantities such as its moments and its spectrum. In particular this last concept is introduced with clear and explicit reference to the measurement process. The two-level atom is used as the basic prototype to illustrate the theory in a concrete application. Quantum phenomena appearing in the spectrum of the fluorescence light, such as Mollow’s triplet structure, squeezing of the fluorescence light, and the linewidth narrowing, are presented. Last but not least, the theory of quantum continuous measurements is the natural starting point to develop a feedback control theory in continuous time for quantum systems. The two-level atom is again used to introduce and study an example of feedback based on the observed output.
Author: Alberto Barchielli
Publisher: Springer Science & Business Media
ISBN: 3642012973
Category : Mathematics
Languages : en
Pages : 331
Get Book Here
Book Description
This course-based monograph introduces the reader to the theory of continuous measurements in quantum mechanics and provides some benchmark applications. The approach chosen, quantum trajectory theory, is based on the stochastic Schrödinger and master equations, which determine the evolution of the a-posteriori state of a continuously observed quantum system and give the distribution of the measurement output. The present introduction is restricted to finite-dimensional quantum systems and diffusive outputs. Two appendices introduce the tools of probability theory and quantum measurement theory which are needed for the theoretical developments in the first part of the book. First, the basic equations of quantum trajectory theory are introduced, with all their mathematical properties, starting from the existence and uniqueness of their solutions. This makes the text also suitable for other applications of the same stochastic differential equations in different fields such as simulations of master equations or dynamical reduction theories. In the next step the equivalence between the stochastic approach and the theory of continuous measurements is demonstrated. To conclude the theoretical exposition, the properties of the output of the continuous measurement are analyzed in detail. This is a stochastic process with its own distribution, and the reader will learn how to compute physical quantities such as its moments and its spectrum. In particular this last concept is introduced with clear and explicit reference to the measurement process. The two-level atom is used as the basic prototype to illustrate the theory in a concrete application. Quantum phenomena appearing in the spectrum of the fluorescence light, such as Mollow’s triplet structure, squeezing of the fluorescence light, and the linewidth narrowing, are presented. Last but not least, the theory of quantum continuous measurements is the natural starting point to develop a feedback control theory in continuous time for quantum systems. The two-level atom is again used to introduce and study an example of feedback based on the observed output.
Author: Pratim Kumar Chattaraj
Publisher: CRC Press
ISBN: 1439825629
Category : Mathematics
Languages : en
Pages : 412
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Book Description
The application of quantum mechanics to many-particle systems has been an active area of research in recent years as researchers have looked for ways to tackle difficult problems in this area. The quantum trajectory method provides an efficient computational technique for solving both stationary and time-evolving states, encompassing a large area o
Author: Robert E. Wyatt
Publisher: Springer Science & Business Media
ISBN: 0387281452
Category : Mathematics
Languages : en
Pages : 425
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Book Description
This is a rapidly developing field to which the author is a leading contributor New methods in quantum dynamics and computational techniques, with applications to interesting physical problems, are brought together in this book Useful to both students and researchers
Author: Miguel Orszag
Publisher: Springer Science & Business Media
ISBN: 9783540650089
Category : Science
Languages : en
Pages : 396
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Book Description
Quantum Optics gives a very broad coverage of basic laser-related phenomena that allow scientists and engineers to carry out research in quantum optics and laser physics. It covers the quantization of the electromagnetic field, quantum theory of coherence, atom-field interaction models, resonance fluorescence, quantum theory of damping, laser theory using both the master equation and the Langevin approach, the correlated-emission laser, input-output theory with application in nonlinear optics, quantum trajectories, atom optics, quantum non-demolition measurements and generation of non-classical vibrational states of ions in a Paul trap. These topics are presented in a unified and didactic manner. The presentation of the book is clear and pedagogical; it balances the theoretical aspects of the optical phenomena with recent relevant experiments.
Author: Howard M. Wiseman
Publisher: Cambridge University Press
ISBN: 0521804426
Category : Mathematics
Languages : en
Pages : 477
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Book Description
Modern quantum measurement for graduate students and researchers in quantum information, quantum metrology, quantum control and related fields.
Author: Kurt Jacobs
Publisher: Cambridge University Press
ISBN: 1139992198
Category : Science
Languages : en
Pages : 729
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Book Description
Recent experimental advances in the control of quantum superconducting circuits, nano-mechanical resonators and photonic crystals has meant that quantum measurement theory is now an indispensable part of the modelling and design of experimental technologies. This book, aimed at graduate students and researchers in physics, gives a thorough introduction to the basic theory of quantum measurement and many of its important modern applications. Measurement and control is explicitly treated in superconducting circuits and optical and opto-mechanical systems, and methods for deriving the Hamiltonians of superconducting circuits are introduced in detail. Further applications covered include feedback control, metrology, open systems and thermal environments, Maxwell's demon, and the quantum-to-classical transition.
Author: Vlad Stefan Barbu
Publisher: John Wiley & Sons
ISBN: 1786306034
Category : Mathematics
Languages : en
Pages : 288
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Book Description
This book is a collective volume authored by leading scientists in the field of stochastic modelling, associated statistical topics and corresponding applications. The main classes of stochastic processes for dependent data investigated throughout this book are Markov, semi-Markov, autoregressive and piecewise deterministic Markov models. The material is divided into three parts corresponding to: (i) Markov and semi-Markov processes, (ii) autoregressive processes and (iii) techniques based on divergence measures and entropies. A special attention is payed to applications in reliability, survival analysis and related fields.
Author: Yu Zheng
Publisher: Springer Science & Business Media
ISBN: 1461416299
Category : Computers
Languages : en
Pages : 328
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Book Description
Spatial trajectories have been bringing the unprecedented wealth to a variety of research communities. A spatial trajectory records the paths of a variety of moving objects, such as people who log their travel routes with GPS trajectories. The field of moving objects related research has become extremely active within the last few years, especially with all major database and data mining conferences and journals. Computing with Spatial Trajectories introduces the algorithms, technologies, and systems used to process, manage and understand existing spatial trajectories for different applications. This book also presents an overview on both fundamentals and the state-of-the-art research inspired by spatial trajectory data, as well as a special focus on trajectory pattern mining, spatio-temporal data mining and location-based social networks. Each chapter provides readers with a tutorial-style introduction to one important aspect of location trajectory computing, case studies and many valuable references to other relevant research work. Computing with Spatial Trajectories is designed as a reference or secondary text book for advanced-level students and researchers mainly focused on computer science and geography. Professionals working on spatial trajectory computing will also find this book very useful.
Author: Howard Carmichael
Publisher: Springer Science & Business Media
ISBN: 3540476202
Category : Science
Languages : en
Pages : 192
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Book Description
This volume contains ten lectures presented in the series ULB Lectures in Nonlinear Optics at the Universite Libre de Bruxelles during the period October 28 to November 4, 1991. A large part of the first six lectures is taken from material prepared for a book of somewhat larger scope which will be published,by Springer under the title Quantum Statistical Methods in Quantum Optics. The principal reason for the early publication of the present volume concerns the material contained in the last four lectures. Here I have put together, in a more or less systematic way, some ideas about the use of stochastic wavefunctions in the theory of open quantum optical systems. These ideas were developed with the help of two of my students, Murray Wolinsky and Liguang Tian, over a period of approximately two years. They are built on a foundation laid down in a paper written with Surendra Singh, Reeta Vyas, and Perry Rice on waiting-time distributions and wavefunction collapse in resonance fluorescence [Phys. Rev. A, 39, 1200 (1989)]. The ULB lecture notes contain my first serious atte~pt to give a complete account of the ideas and their potential applications. I am grateful to Professor Paul Mandel who, through his invitation to give the lectures, stimulated me to organize something useful out of work that may, otherwise, have waited considerably longer to be brought together.
Author: David W. Snoke
Publisher: Cambridge University Press
ISBN: 100926155X
Category : Science
Languages : en
Pages : 341
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Book Description
