A Measure Theoretical Approach to Quantum Stochastic Processes (Lecture Notes in Physics Book 878) 2014th Edition by Wilhelm Waldenfels (PDF)

Description

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.

User’s Reviews

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⭐This book is aimed at mathematical physicists interested in the mathematical formulation of quantum stochastic processes. Unlike the book by Meyer on general aspects of quantum probability, this monograph centres squarely on the Hudson-Parthasarathy theory and is motivated mainly by physical models of open markovian quantum systems that have become increasingly important in modelling open quantum optics. At its heart, this book deals with the Hamiltonian description of quantum stochastic models and gives a rigorous construction through calculating the resolvent. The techniques may be mathematically involved, for instance the use of kernel calculus, but this remarkable book will reward the reader with a treasure trove of insights to a beautiful and powerful theory, much of which is due to Prof. von Waldenfels. Several exactly solvable examples illustrate the physical relevance of the results derived here. The monograph is a clear and self-contained account of Prof. von Waldenfels’ deep and important contribution to quantum stochastic processes as a branch of mathematical physics.

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