Positrons vs electrons channeling in silicon crystal: energy levels, wave functions and quantum chaos manifestations

TL;DR

This study investigates quantum chaos in the axial channeling of electrons and positrons in silicon crystals, analyzing energy levels, wave functions, and the impact of chaotic motion on their quantum states.

Contribution

It provides a detailed numerical analysis of energy spectra and wave functions for electrons and positrons, highlighting differences in chaos manifestation and applying group theory for eigenfunction classification.

Findings

Positron channeling exhibits widespread chaos across initial conditions.

Electrons show limited chaotic regions in phase space.

Channeling radiation spectrum computed for low-energy electrons.

Abstract

The motion of fast electrons through the crystal during axial channeling could be regular and chaotic. The dynamical chaos in quantum systems manifests itself in both statistical properties of energy spectra and morphology of wave functions of the individual stationary states. In this report, we investigate the axial channeling of high and low energy electrons and positrons near [100] direction of a silicon crystal. This case is particularly interesting because of the fact that the chaotic motion domain occupies only a small part of the phase space for the channeling electrons whereas the motion of the channeling positrons is substantially chaotic for the almost all initial conditions. The energy levels of transverse motion, as well as the wave functions of the stationary states, have been computed numerically by the method presented at previous RREPS. Note that the potential of the elementary cell in (100) plane of silicon crystal possesses the symmetry of the square. The group theory methods had been used for classification of the computed eigenfunctions and identification of the non-degenerate and doubly degenerate energy levels. The channeling radiation spectrum for the low energy electrons has been also computed.