Abstract

In recent years, progress has been made in understanding the status of random matrix theory in the physics of classically chaotic quantum systems by methods of semiclassical analysis. We owe much of this progress to the linkage between semiclassical expansions in terms of periodic orbits on the one hand, and field theoretical methods (integration over certain sigma model manifolds) on the other hand. I will review this connection, special emphasis put on the role of a stationary point in the domain of integration, the Altshuler Andreev saddle point. This point had long been reckognized as instrumetal in understanding the non-perturbative aspects of spectral statistics (the sine-kernel, for instance.) The recently constructed semiclassical analogies have offered the possibility to understand its role in more intuitive terms, to be discussed in the talk.