Lecture Notes in Physics

Waldenfels, Wilhelm

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.

Details

Published by: Springer

Publication Date: 2013-12-12

Format: Paperback

ISBN-13: 9783642450815

DOI: 10.1007/978-3-642-45082-2

Dimensions: 235cm x155cm

Pages: 228