Colloquium on May 14th, 2007

Steven Tomsovic, Washington State University
Martin Gutzwiller Fellowship, Award Ceremony

An Irreversibility Paradox in Simple Chaotic Systems

The term irreversibility usually evokes the inability of thermodynamics to be reversed. However, it may also refer to the inability of even quite simple dynamical systems to retrace their evolution if they are not perfectly controlled. Indeed, the fidelity is designed to measure this brand of irreversibility. It turns out that simple, classically chaotic systems are effectively irreversible whereas their quantum counterparts are quite reversible. It is therefore paradoxical that it has been shown, via semiclassical theory, that classical dynamics can be used to construct excellent approximations of quantum dynamics for long time scales under these circumstances; i.e. how can it make sense that an irreversible dynamics reconstructs accurately a reversible dynamics. We discuss the resolution of this paradox and its relation to the structural stability inherent in classically chaotic systems in spite of their individual trajectories' exponential sensitivity to initial conditions.