Signatures of strange nonchaotic dynamics in a forced quantum system.

Abstract

Can strange sets arise out of quantum dynamics? We explore this question using the quantum analog of a classical impact oscillator, which consists of a forced spring-mass-damper system, with a wall it may collide against. The classical impact oscillator is known to undergo a sudden transition to chaos when the mass grazes the wall. We numerically compute the evolution of the wave function in the equivalent quantum system and investigate the dynamical signatures. The entropy of the probability density and the L_{1} norm are used to generate real-valued time series, which are then subjected to diagnostic tests. Even though closed quantum systems with unitary evolution are incapable of showing chaotic behavior, we observe the characteristic features of strange nonchaotic dynamics in the forced system.