On the complexity of the positron’s dynamics in a short carbon nanotube: a full explanation of the rainbow effect

Abstract

This paper contains the results of the classical, uniform semiclassical, and quantum mechanical study of the channeling of 1 MeV positrons in a short (11, 9) chiral carbon nanotube. In the classical part of the study, we have analyzed the positron trajectories, which reveal the existence of the primary, secondary, and higher-order rainbow lines. The semiclassical part of the study has been performed with the incident positron represented as a plane wave, while in the fully quantum approach, by a wide Gaussian wave packet. In the former case, only the primary rainbow exists; in the latter, the higher-order rainbows also appear. The evolution of the semiclassical spatial distribution of channeled positrons reveals that rainbow and dislocation points are organized in lines. These points and lines are recognized in the evolution of the quantum spatial distribution of channeled positrons. In the quantum party of the study, special attention has been paid to the Bohm positron trajectories and their finite-time Lyapunov exponents. We demonstrate that the classical, semiclassical, and quantum rainbow effects are complex and catastrophic. These results explain entirely the rainbow effect in the positron transmission through the nanotube.