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Physics - Quantum Physics | A Measure Theoretical Approach to Quantum Stochastic Processes

A Measure Theoretical Approach to Quantum Stochastic Processes

Series: Lecture Notes in Physics, Vol. 878

Waldenfels, Wilhelm

2014, XVII, 228 p.

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  • Authored by a leading researcher in the field
  • Self-contained presentation of the subject matter
  • Examines a number of worked examples in detail
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.

Content Level » Research

Keywords » Classical measure theory - Hudson-Parthasarathy equation - Quantum stochastic processes - Spectral decomposition of Hamilton operator - White noise calculus

Related subjects » Quantum Physics - Theoretical, Mathematical & Computational Physics

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