Holon Physics Seminar

 

 

In plain words chaos refers to extreme dynamical instability and unpredictability. Yet in spite of such inherent instability, quantum systems with classically chaotic dynamics exhibit remarkable universality. In particular, their energy levels often display the universal statistical properties which can be effectively described by Random Matrix Theory.

 

From the semiclassical point of view this remarkable phenomenon can be attributed to the existence of pairs of classical periodic 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 recent efforts to extend this program to a class of systems with a very large number of particles. The crucial ingredient of our approach is a two-dimensional symbolic dynamics which allows an effective representation of periodic orbits and their pairings. I will illustrate the theory with a specific model of coupled cat maps, where such a symbolic dynamics can be constructed explicitly.