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Quantum Trajectories and Measurements in Continuous Time

The Diffusive Case

  • Book
  • © 2009

Overview

Authors:
  1. Alberto Barchielli

    1. Dipto. Matematica, Politecnico di Milano, Milano, Italy

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  2. Matteo Gregoratti

    1. Dipto. Matematica, Politecnico di Milano, Milano, Italy

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    You can also search for this author in PubMed   Google Scholar

Part of the book series: Lecture Notes in Physics (LNP, volume 782)

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Table of contents (10 chapters)

  1. Front Matter

    Pages i-xiii
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  2. Introduction

    • Alberto Barchielli, Matteo Gregoratti
    Pages 1-7

  3. General Theory

    1. Front Matter

      Pages 9-9
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  4. Part I General theory

    1. The Stochastic Schrödinger Equation

      • Alberto Barchielli, Matteo Gregoratti
      Pages 11-49

    2. The Stochastic Master Equation: Part I

      • Alberto Barchielli, Matteo Gregoratti
      Pages 51-75

    3. Continuous Measurements and Instruments

      • Alberto Barchielli, Matteo Gregoratti
      Pages 77-110

    4. The Stochastic Master Equation: Part II

      • Alberto Barchielli, Matteo Gregoratti
      Pages 111-123

    5. Mutual Entropies and Information Gain in Quantum Continuous Measurements

      • Alberto Barchielli, Matteo Gregoratti
      Pages 125-142

  5. Physical Applications

    1. Front Matter

      Pages 143-143
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  6. Part II Physical applications

    1. Quantum Optical Systems

      • Alberto Barchielli, Matteo Gregoratti
      Pages 145-150

    2. A Two-Level Atom: General Setup

      • Alberto Barchielli, Matteo Gregoratti
      Pages 151-182

    3. A Two-Level Atom: Heterodyne and Homodyne Spectra

      • Alberto Barchielli, Matteo Gregoratti
      Pages 183-220

    4. Feedback

      • Alberto Barchielli, Matteo Gregoratti
      Pages 221-262

  7. Back Matter

    Pages 1-61
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Keywords

About this book

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.

Reviews

From the reviews:

“This quite interesting book is devoted to the theory of continuous measurements in quantum mechanics. … aimed at both mathematicians and physicists, keeping together mathematical rigor and physical motivation. … The presentation ends with two very well written and useful appendixes, providing a brief and self-contained introduction to stochastic differential equations as well as the general formulation of quantum mechanics. … these two appendixes are meant to help the physicists or the mathematicians which are not confident with the formalism or the physical interpretation, respectively.” (Bassano Vacchini, Zentralblatt MATH, Vol. 1182, 2010)

“This monograph is intended principally for researchers in theoretical quantum optics and related fields. … The book is well structured and the presentation is excellent. The mathematics is developed rigorously and without compromise: the physical interpretation is always kept to the fore. … Anyone interested in quantum trajectory theory will find this work a most useful introduction.” (Alexander C. R. Belton, Mathematical Reviews, January, 2013)

Authors and Affiliations

  • Dipto. Matematica, Politecnico di Milano, Milano, Italy

    Alberto Barchielli, Matteo Gregoratti

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