Quantum response to classical transitions.

Abstract

The richness and complexity of two-dimensional parameter space of the kicked Harper model is exploited to demonstrate quantum fingerprints of all classical transitions. The quantum system appears to follow the corresponding classical system in parameter but not in time in the localized, critical as well as in the ballistic regimes. Therefore, the relationship between quantum and classical systems appears to be universal when measured by their response to parameter changes. Additionally, a rather intriguing feature of quantum eigenstates is a set of critical points sprinkled in the regime where the classical dynamics is diffusive. These are the boundary points of the ballistic (localized) patches in the localized (ballistic) regime that survive in the semiclassical limit.