Recurrent versus diffusive dynamics for a kicked quantum system

Amit Kumar Anand, J. Davis, Shohini Ghose

The emergence of classical chaos from an underlying quantum mechanics remains a challenging question due to the differences between dynamics driven by Schrödinger's equation versus Newton's equations. We present an infinite family of purely quantum recurrences that are not present in the classical limit of a chaotic system. They take the form of stroboscopic unitary evolutions in the quantum kicked top that act as the identity after a finite number of kicks. These state-independent recurrences are present in all finite dimensions and depend on the strength of the chaoticity parameter of the top. We further discuss the relationship of these periodicities to the quantum kicked rotor dynamics and the phenomenon of quantum antiresonance. Published by the American Physical Society 2024

Lit-Deh Chang

Gerard J Milburn

The quantum dynamics of periodically kicked hamiltonian systems can reflect the classical dynamics be it regular or chaotic. However in quantum systems the classical chaotic diffusion of one phase space variable is suppressed due to irregular recurrences in the quantum state. This aspect of quantum nonlinear dynamics should be accessible to experimental test and recent results on the microwave ionization of hydrogen would seem to confirm it.

M. Vubangsi, Martin Tchoffo, Lukong Cornelius Fai

Alexey Vyacheslavovich Gorshkov

Theo Geisel

A two-level system subject to quasiperiodically modulated kicking is investigated under the aspects of ergodic theory. For weak kicking strength \ensuremath{\kappa} the correlation functions exhibit quasiperiodic behavior, whose character changes with increasing \ensuremath{\kappa} as recurrences become infrequent. A quantum instability with a transition to mixing behavior that was suggested for similar models does not arise. Analytic results are obtained for the case where two of three characteristic frequencies are incommensurate.