Wilhelm von Waldenfels

Quantum independent increment processes on superalgebras

On introduit la notion de processus quantique independant a increment stationnaire sur des superalgebres et on demontre un theoreme de reconstruction qui etablit une correspondance un-a-un entre ces processus et leurs generateurs infinitesimaux

Stochastic Properties of the Radiative Transfer Equation

Radiative transfer is connected with Markov processes in two ways. The usual transfer equation corresponds to a process with five dimensional state space in continuous time, the Milne’s equation corresponds to process in three dimensional state space in discrete time.

Derivation of the Radiative Transfer Equation for Polarized Light

The transfer equation for polarized light is related to a non‐commutative Markov process. Using scattering by two level atoms, where the lower state is an s‐state and the upper state is a p‐state, and the limits of geometrical optics and singular coupling and assuming, that the scatterers form a Poisson point process, the infinitesimal law of the Markov process can be determined. That is equivalent to the transfer equation.

An Example of the Singular Coupling Limit

We consider the stochastic differential equation

The singular coupling limit for a simple pure number process

\frac{{dU_{s}^{t}}}{{dt}} = ({{L}_{0}}F(t) + {{L}_{1}}{{F}^{ + }}(t))U_{s}^{t}

Quantum Probability and Applications III

where

A central limit theorem on the free lie group

F(t) = \int {g(t - s){{a}_{s}}ds}