Author : Pratim Kumar Chattaraj
Publisher : CRC Press
Page : 412 pages
File Size : 28,26 MB
Release : 2016-04-19
Category : Mathematics
ISBN : 1439825629
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 : Alberto Barchielli
Publisher : Springer Science & Business Media
Page : 331 pages
File Size : 33,82 MB
Release : 2009-07-21
Category : Mathematics
ISBN : 3642012973
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 : Robert E. Wyatt
Publisher : Springer Science & Business Media
Page : 425 pages
File Size : 30,58 MB
Release : 2006-05-28
Category : Mathematics
ISBN : 0387281452
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 : Alberto Barchielli
Publisher : Springer
Page : 331 pages
File Size : 15,5 MB
Release : 2009-07-11
Category : Science
ISBN : 3642012981
Quantum trajectory theory is largely employed in theoretical quantum optics and quantum open system theory and is closely related to the conceptual formalism of quantum mechanics (quantum measurement theory). However, even research articles show that not all the features of the theory are well known or completely exploited. We wrote this monograph mainly for researchers in theoretical quantum optics and related ?elds with the aim of giving a self-contained and solid p- sentation of a part of quantum trajectory theory (the diffusive case) together with some signi?cant applications (mainly with purposes of illustration of the theory, but which in part have been recently developed). Another aim of the monograph is to introduce to this subject post-graduate or PhD students. To help them, in the most mathematical and conceptual chapters, summaries are given to ?x ideas. Moreover, as stochastic calculus is usually not in the background of the studies in physics, we added Appendix A to introduce these concepts. The book is written also for ma- ematicians with interests in quantum theories. Quantum trajectory theory is a piece of modern theoretical physics which needs an interplay of various mathematical subjects, such as functional analysis and probability theory (stochastic calculus), and offers to mathematicians a beautiful ?eld for applications, giving suggestions for new mathematical developments.
Author : Miguel Orszag
Publisher : Springer
Page : 491 pages
File Size : 37,5 MB
Release : 2016-04-18
Category : Science
ISBN : 3319290371
This new edition gives a unique and broad coverage of basic laser-related phenomena that allow graduate students, scientists and engineers to carry out research in quantum optics and laser physics. It covers 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 theory, the correlated emission laser, input-output theory with applications to non-linear optics, quantum trajectories, quantum non-demolition measurements and generation of non-classical vibrational states of ions in a Paul trap. In this third edition, there is an enlarged chapter on trapped ions, as well as new sections on quantum computing and quantum bits with applications. There is also additional material included for quantum processing and entanglement. These topics are presented in a unified and didactic manner, each chapter is accompanied by specific problems and hints to solutions to deepen the knowledge.
Author : Howard M. Wiseman
Publisher : Cambridge University Press
Page : 477 pages
File Size : 29,65 MB
Release : 2010
Category : Mathematics
ISBN : 0521804426
Modern quantum measurement for graduate students and researchers in quantum information, quantum metrology, quantum control and related fields.
Author : Ángel S. Sanz
Publisher : Springer
Page : 345 pages
File Size : 10,98 MB
Release : 2013-09-13
Category : Science
ISBN : 3642179746
Trajectory-based formalisms are an intuitively appealing way of describing quantum processes because they allow the use of "classical" concepts. Beginning as an introductory level suitable for students, this two-volume monograph presents (1) the fundamentals and (2) the applications of the trajectory description of basic quantum processes. This second volume is focussed on simple and basic applications of quantum processes such as interference and diffraction of wave packets, tunneling, diffusion and bound-state and scattering problems. The corresponding analysis is carried out within the Bohmian framework. By stressing its interpretational aspects, the book leads the reader to an alternative and complementary way to better understand the underlying quantum dynamics.
Author : Howard J. Carmichael
Publisher : Springer Science & Business Media
Page : 551 pages
File Size : 15,70 MB
Release : 2007-10-23
Category : Science
ISBN : 3540713190
This second volume of Howard Carmichael’s work continues the development of the methods used in quantum optics to treat open quantum systems and their fluctuations. Its early chapters build upon the phase-space methods introduced in Volume 1. Written on a level suitable for debut researchers or students in an advanced course in quantum optics, or a course in quantum mechanics or statistical physics that deals with open quantum systems.
Author : Kurt Jacobs
Publisher : Cambridge University Press
Page : 729 pages
File Size : 37,47 MB
Release : 2014-08-14
Category : Science
ISBN : 1139992198
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
Page : 288 pages
File Size : 21,98 MB
Release : 2020-12-03
Category : Mathematics
ISBN : 1786306034
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.
