A Measure Theoretical Approach to Quantum Stochastic Processes

ISBN-13: 9783642450815 / Angielski / Miękka / 2013 / 228 str.

Wilhelm Waldenfels

Opis

This monograph takes as starting point that abstract quantum stochastic processes can be understood as a quantum field theory in one space and in one time coordinate. As a result it is appropriate to represent operators as power series of creation and annihilation operators in normal-ordered form, which can be achieved using classical measure theory.Considering in detail four basic examples (e.g. a two-level atom coupled to a heat bath of oscillators), in each case the Hamiltonian of the associated one-parameter strongly continuous group is determined and the spectral decomposition is explicitly calculated in the form of generalized eigen-vectors.Advanced topics include the theory of the Hudson-Parthasarathy equation and the amplified oscillator problem. To that end, a chapter on white noise calculus has also been included.

Recenzje

From the book reviews:

"This monograph represents a nice survey written in a concise and lucid manner, enabling the reader to quickly and easily grasp the main aspects and ideas of quantum stochastic processes. ... The book is suitable for graduate students or researchers who work in the field of mathematics and physics." (Dora Selesi, Mathematical Reviews, February, 2015)

Spis treści

Weyl Algebras.- Continuous Sets of Creation and Annihilation Operators.- One-Parameter Groups.- Four Explicitly Calculable One-Excitation Processes.- White Noise Calculus.- Circled Integrals.- White Noise Integration.- The Hudson-Parthasarathy Differential Equation.- The Amplifies Oscillator.- Approximation by Coloured Noise.- Index.