Mathematical Physics

Contact : Prof R Duvenhage
 

Research Interests

• Mathematical structure of quantum dynamical systems in the framework of operator algebras.
• Quantum (that is to say, noncommutative) ergodic theory and its connections with quantum statistical mechanics.
• Quantization in the framework of operator algebras.
• High energy physics and string theory.

Research Projects
 

• Noncommutative ergodic theory and quantum statistical mechanics

Ergodic theory concerns the long term behaviour of dynamical systems, and is closely related to statistical mechanics. In our research we systematically and rigorously study ergodic problems in the quantum case.

• Quantum groups and their actions. Field theory and string theory on quantum spaces.

These topics share many ideas and techniques with topic 1 above. Our focus is on the mathematical aspects of these topics, especially those aspects closely related to topic above.

Local collaboration

Conrad Beyers and Anton Ströh (Department of Mathematics and Applied
Mathematics, UP)
Richard de Beer (Unisa)
Robert de Mello Koch (Department of Physics, Wits)
 

International collaboration

László Zsidó and Francesco Fidaleo (Dipartimento di Matematica,Universita' Degli Studi di Roma "Tor Vergata", Roma, Italia)
 

Recent publications

Beyers, Conrad; Duvenhage, Rocco; Ströh, Anton. The Szemerédi property in ergodic W*-dynamical systems. J. Operator Theory (to appear).

Duvenhage, Rocco. Bergelson's theorem for weakly mixing C*-dynamical systems.  Studia Math. 192 (2009),  no. 3, 235257.

Duvenhage, Rocco. A mean ergodic theorem for actions of amenable quantum groups. Bull. Aust. Math. Soc.  78  (2008),  no. 1, 8795.

Duvenhage, Rocco. Evolution integrals. J. Operator Theory  60  (2008), no. 1, 199215.
               
Duvenhage, Rocco. Joinings of W*-dynamical systems. J. Math. Anal. Appl.  343  (2008),  no. 1, 175181.
               
de Beer, Richard;  Duvenhage, Rocco;  Ströh, Anton. Noncommutative recurrence over locally compact Hausdorff groups. J. Math. Anal. Appl. 322  (2006),  no. 1, 6674.
               
Duvenhage, Rocco;  Ströh, Anton. Recurrence and ergodicity in unital *-algebras. J. Math. Anal. Appl.  287  (2003),  no. 2, 430443.
               
Duvenhage, Rocco. The nature of information in quantum mechanics. Found. Phys.  32  (2002),  no. 9, 13991417.
               
Duvenhage, Rocco. Recurrence in quantum mechanics. Internat. J. Theoret. Phys.  41  (2002),  no. 1, 4561.