BIBFRAME Work

Title

A Measure Theoretical Approach to Quantum Stochastic Processes

Type

  • Text
  • Monograph

Contribution

Waldenfels, Wilhelm (author)

Subject

Language

Classification

Content

Summary

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.

Table of Contents

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.

Authorized Access Point

Waldenfels, Wilhelm. A Measure Theoretical Approach to Quantum Stochastic Processes

Admin Metadata

  • Date: 2026-09-11T20:21:17.356294+00:00
  • Agent: cbc
  • Status: c
  • Derived from: 21821761

Admin Metadata

  • Date: 2026-09-11
  • Cataloger id: Unknown
  • Description level: http://id.loc.gov/ontologies/bibframe-2-6-0/
  • Description language: eng
  • Description authentication: pcc

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