A Measure Theoretical Approach to Quantum Stochastic Processes (Lecture Notes in Physics #878)

By: Wilhelm Waldenfels

Sign Up Now! Already a Member? Log In
You must be logged into Bookshare to access this title. Learn about membership options, or view our freely available titles.

Synopsis: 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.