Department of Analysis und Mathematical Physics
Research 1993-95
Project:
Quantum Probability
Participants:
GOHM, R. (Dr.rer.nat.)
HELLMICH, J. (Dipl. Phys.)
HERTFELDER, C. (Dipl. Phys.)
HINZ, J. (Dipl. Math.)
KÖSTLER, C. (Dipl. Phys.)
KÜMMERER, B.
(Prof. Dr.rer.nat.)
RIECKERS, A. (Prof. Dr.rer.nat., Institut für Theoret. Physik)
RUPP, C. (Dr.rer.nat.)
SCHWEIZER, J. (Dipl. Math.)
WOLFF, M. (Prof. Dr.rer.nat.)
together with:
MAASSEN, H. (Dozent Dr., Univ. Nijmegen, Netherlands)
SPEICHER, R. (Dozent Dr.rer.nat., Univ. Heidelberg)
Text:
The main concern of the theory of quantum probability is to describe stochastic
influences of quantum mechanical systems upon each other. To accomplish this,
an extension of the mathematical formalism of classical probability theory is
necessary, and a suitable frame is provided by the theory of operator algebras.
The work done in the reported time period centers around the so called
coupling representations of quantum stochastic processes (Markovian or non-Markovian).
Often the existence of a coupling representation has to be proved with
cohomological means. It makes possible an interpretation of the process as a
description of an open system under stochastic influence (white or coloured noise).
In many cases the process may be obtained as a solution of a stochastic differential
equation. There are also other directions of study of these processes which are
opened by coupling representations, for example the calculation of their entropy.
DFG, HCM (Human Capital and Mobility Program),
Grad. Förderung, Studienstiftung, VILLIGST
Key Publication:
Kümmerer, B., Speicher, R.;
Stochastic integration on the Cuntz algebra.
J. Funct. Anal. 103, 373-408 (1992).
Another introductory text (in german):
Nichtkommutative Wahrscheinlichkeitstheorie und Quantenstochastik
Rolf Gohm
rolf.gohm@uni-tuebingen.de