School of Physics Nonlinear Science & Mathematical Physics: Prof. Boris Gutkin, Visiting Professor, Center for Nonlinear Science

Quantum systems with the underlying classical chaotic dynamics exhibit universal spectral and transport properties effectively described by Random Matrix Theory. In the last decade this remarkable phenomenon found a semiclassical explanation in terms of pairs of classical orbits with small action differences. So far, however, the scope of this theory has, by and large, been restricted to single-particle systems. I will discuss an extension of this program to chaotic systems with a large number of particles. Our approach is based on introduction of two-dimensional symbolic dynamics which allows an effective representation of periodic orbits in many-particle chaotic systems with local homogeneous interactions. Using this representation we show that for a large number of particles the dominant correlation mechanism among periodic orbits essentially differs from the one of the single-particle theory. Its implications on spectral properties of many-particle quantum systems will be discussed as well.