Waldenfels A Measure Theoretical Approach to Quantum Stochastic Processes
Erscheinungsjahr 2013
ISBN: 978-3-642-45082-2
Verlag: Springer
Format: PDF
Kopierschutz: 1 - PDF Watermark
E-Book, Englisch, 228 Seiten
Reihe: Physics and Astronomy
ISBN: 978-3-642-45082-2
Verlag: Springer
Format: PDF
Kopierschutz: 1 - PDF Watermark
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.
Zielgruppe
Research
Autoren/Hrsg.
Weitere Infos & Material
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.
