The helical quantum two-body problem and its wave packet dynamics

TL;DR

This paper investigates the quantum dynamics of two particles on a helix with tunable potential wells, revealing complex wave packet behaviors like oscillations, beats, and pulsed emissions influenced by the multi-well landscape.

Contribution

It introduces a detailed analysis of the helical quantum two-body problem, highlighting how the geometry-induced potential wells affect wave packet dynamics and transient evolution.

Findings

Multi-well potential landscape causes complex oscillatory patterns.

Wave packets exhibit beats and pulsed emissions due to intrawell dynamics.

Potential well properties depend on helix geometry, influencing quantum behavior.

Abstract

We explore the helical quantum two-body problem i.e. two repulsively Coulomb interacting particles confined to move along a helix. The effective potential possesses a tunable number of potential wells superimposed on the repulsive Coulomb interaction that can be varied by changing the ratio of the pitch and radius of the helix. The anharmonicity of these wells depends crucially on this ratio and on the order of the well which can be seen also by analyzing the individual wells energy eigenvalue spacing. Our main focus is the investigation of the quantum dynamics of differently prepared wave packets that scatter from the multi-well potential landscape. We show that there exists a rich pattern forming transient evolution which depends also on the number of bound states of the individual wells. We demonstrate how the multiple wells leave their fingerprints in the dynamics leading, among others, to oscillatory structures on different spatial scales, the formation of beats and pulsed emission from single well localized wave packets due to their intrawell dynamics.