# A Measure Theoretical Approach to Quantum Stochastic Processes [electronic resource] /

##### by Waldenfels, Wilhelm [author.]; SpringerLink (Online service).

Material type: BookSeries: Lecture Notes in Physics: 878Publisher: Berlin, Heidelberg : Springer Berlin Heidelberg : 2014.Description: XVII, 228 p. online resource.ISBN: 9783642450822.Subject(s): Physics | Quantum theory | Mathematical physics | Physics | Quantum Physics | Mathematical Physics | Mathematical Methods in PhysicsDDC classification: 530.12 Online resources: Click here to access onlineItem type | Current location | Call number | Status | Date due | Barcode |
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E-Books |
Central Library, IISER Bhopal
OPAC URL: http://webopac.iiserb.ac.in/ |
530.12 (Browse shelf) | Not for loan |

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.

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.

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