# Low-Dimensional Few-Body Processes in Confined Geometry of Atomic and Hybrid Atom-Ion Traps

## TL;DR

This paper presents an efficient computational approach for analyzing low-dimensional few-body quantum processes in atomic and hybrid atom-ion traps, enabling better understanding of ultracold atomic interactions in confined geometries.

## Contribution

The authors introduce a split-operator method in 2D DVR for solving the time-dependent Schrödinger equation in low-dimensional systems, advancing computational techniques in this field.

## Key findings

- Application to resonant ultracold atomic processes demonstrated
- Results on hybrid atomic-ion systems discussed
- Method shows promise for other low-dimensional few-particle problems

## Abstract

We have developed an efficient approach for treating low-dimensional few-body processes in confined geometry of atomic and hybrid atom-ion traps. It based on the split-operator method in 2D discrete-variable representation (DVR) suggested by V. Melezhik for integration of the few-dimensional time-dependent Schr\"odinger equation. We give a brief review of the application to resonant ultracold atomic processes and discuss our latest results on hybrid atomic-ion systems. Prospects for the application of the method in other hot problems of the physics of low-dimensional few-particle systems are also discussed.