Random-matrix theories in quantum physics : common concepts

We review the development of random-matrix theory (RMT) during the last decade. We emphasize both the theoretical aspects, and the application of the theory to a number of fields. These comprise chaotic and disordered systems, the localization problem, many-body quantum systems, the Calogero-Sutherland model, chiral symmetry breaking in QCD, and quantum gravity in two dimensions. The review is preceded by a brief historical survey of the developments of RMT and of localization theory since their inception. We emphasize the concepts common to the above-mentioned fields as well as the great diversity of RMT. In view of the universality of RMT, we suggest that the current development signals the emergence of a new "statistical mechanics": Stochasticity and general symmetry requirements lead to universal laws not based on dynamical principles.

Random Matrix Theories in Quantum Physics: Common Concepts

http://www.gbv.de/dms/hebis-darmstadt/toc/113948433.pdf

The Problem of Integrable Discretization: Hamiltonian Approach

Collisions of Calogero-Moser particles and an adelic Grassmannian

We give a review of the mathematical and physical properties of the celebrated family of Calogero-like models and related spin chains.

Theo Hermsen

Papers

A generalisation of the Calogero-Moser system

A Bäcklund transformation for a generalised Calogero-Moser system