Super revivals and sub-Planck scale structures of a slightly relativistic particle in a box

Abstract

The time evolution of a particle, caught in an infinitely deep square well, displays unexpected features, when one includes tiny relativistic effects. Indeed, even the smallest corrections to the non-relativistic quadratic spectrum manifest themselves in a dramatic way. Our theoretical analysis brings to light a completely new time scale, at which the system exhibits surprisingly perfect revivals. This longer time scale rules the system dynamics and replaces the original revival time of the unperturbed system. The early manifestation of such phenomenon is captured by the sensitivity of sub-Planck structures for different values of the relativistic corrections.