## Quantum Trajectories and Measurements in Continuous Time: The Diffusive CaseQuantum 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. |

### What people are saying - Write a review

We haven't found any reviews in the usual places.

### Other editions - View all

Quantum Trajectories and Measurements in Continuous Time: The Diffusive Case Alberto Barchielli,Matteo Gregoratti No preview available - 2009 |

Quantum Trajectories and Measurements in Continuous Time: The Diffusive Case Alberto Barchielli,Matteo Gregoratti No preview available - 2011 |

### Common terms and phrases

atomic squeezing Barchielli Berlin characteristic operator classical coefficients completely positive continuous measurement defined definition density feedback finite dimensional fluorescence light formulation given heterodyne Hilbert space homodyne detection homodyne spectrum inelastic initial condition instrument introduce Lecture Notes linear entropy linear SDE linear stochastic master martingale Math matrix measurable space Moreover mutual entropy nonlinear normalised numbers observed obtain Open Quantum Systems output parameters pathwise unique Phys physical probability posteriori priori Proof properties Proposition quantum dynamical semigroup quantum mechanics quantum optics Quantum Probability quantum stochastic quantum trajectory random variable relative entropy Schrödinger equation Sect semigroups spectral Springer statistical operators stochastic basis stochastic calculus stochastic differential equations stochastic master equation stochastic processes stochastic Schr¨odinger equation stochastic Schrödinger equation Theorem theory two-level atom V. P. Belavkin value space vector Wiener process