November 3-2000:

On November 3, there will be another Mark Kac Seminar. This seminar will
take place on Achter Sint Pieter nr. 200, room 012. Achter Sint Pieter is a street behind the Sint Pieter church in Utrecht.


The speakers are


11:15-13:00 Hans Maassen (Nijmegen)

An ergodic theorem for quantum trajectories.


14:15-16:00 Roberto Fernandez (Universite de Rennes)

Markovian approximations, loss of memory, regeneration 
schemes and perfect simulation





Abstract Hans Maassen:

Uninterrupted observation of a quantum system produces a detection record,
which is a classical stochastic process. We prove that the latter is ergodic
provided that the underlying quantum evolution has this property.
This simple statement has profound significance for experiments such as
photon counting and has in fact always been taken for granted by the physics
community.
Nowadays, the effect of the coupling between a quantum system
and a measurement apparatus is succesfully simulated numerically
by running a Markov chain on the quantum system's state space,
known under the name of `quantum trajectory'. These colourful processes
exhibit the proverbial `quantum jumps', and also perform diffusions. 
Quantum trajectories are quite popular in quantum optics and solid state 
physics. For these trajectories our theorem implies that all statistical 
information obtainable is already contained in a single run.

This is joint work with Burkhard Kuemmerer (Stuttgart).

For more information, see Hans Massen's homepage:

http://www-math.sci.kun.nl/math/~maassen

(see `an ergodic theorem for repeated and continuous measurement').



Abstract Roberto Fernandez:

I shall review the following results, obtained in
collaboration with X. Bressaud, F. Commets, P. Ferrari and A.
Galves, for chains with complete connections with summable memory
decay: 1) Distance ---in \overline d sense--- with the
canonical Markovian approximations. 2) Rate of memory loss of
initial conditions. 3) Regenerative construction and perfect
simulation. These results strengthen previous work by a number of
authors, among them Doeblin, Fortet, Iosifescu, Lalley and Berbee.
Some applications to dynamical systems and random systems with
complete connections will be sketched.