Colloquia: "Random Matrices and Related Topics"

Date and time: 31 January 2001, 16:30

Venue: Room M128, Department of Mathematics, Brunel University (Uxbridge)

Speaker: Dr. T. Guhr (Lund)

"Random Matrix Theory -- Thermodynamics for Spectral Fluctuations?"

Abstract: The energy correlations of a rich variety of different quantum systems show a remarkable degree of universality if the energies are measured on the scale of the local mean level spacing. Random Matrix Theory (RMT) is a simple schematic model which describes these fluctuations. This is discussed for several examples, including quantum chaos, nuclear physics, quantum chromodynamics and elastomechanics(a classical system). Random matrix models are often mathematically demanding: an introduction to concepts such as Dyson's Brownian Motion, a variant of the supersymmetry method and harmonic analysis is also given. After this talk, I can give a presentation on new mathematical results on harmonic analysis in superspaces for those who are interested in these mathematical aspects. I can speak about the theory of super groups, in particular about a new class of Gelfand-Tzetlin coordinates, and about a new recursive structure for matrix Bessel functions which allows one to calculate some of them rather explicitly.