A measure theoretical approach to quantum stochastic processes

• Verfasst von: Waldenfels, Wilhelm von
• Titel: A measure theoretical approach to quantum stochastic processes
• Verf.angabe: by Wilhelm Waldenfels
• Verlagsort: Heidelberg ; New York ; Dordrecht ; London
• Verlag: Springer
• Jahr: 2014
• Umfang: Online-Ressource (XVII, 228 Seiten)
• Gesamttitel/Reihe: Lecture Notes in Physics ; 878
• Gesamttitel/Reihe: SpringerLink : Bücher
• ISBN: 978-3-642-45082-2
• DOI: doi:10.1007/978-3-642-45082-2
• Schlagwörter: (s)Quantenmechanisches System / (s)Stochastische Differentialgleichung / (s)Maßtheorie
• Schlagwörter: (s)Quantenmechanisches System / (s)Stochastische Differentialgleichung / (s)Maßtheorie
• Schlagwörter: (s)Stochastische Quantisierung
• Datenträger: Online-Ressource
• Sprache: eng
• Bibliogr. Hinweis: Erscheint auch als : Druck-Ausgabe: Waldenfels, Wilhelm von, 1932 - 2021: A measure theoretical approach to quantum stochastic processes. - Berlin : Springer, 2014. - XVII, 228 S.
• RVK-Notation: UG 4000
• RVK-Notation: UD 8220
• K10plus-PPN: 1653132280

Abstract

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