# Aharonov-Bohm rings in de Sitter expanding universe

## TL;DR

This paper derives exact relativistic expressions for currents and energies of fermions in Aharonov-Bohm rings within a de Sitter universe, revealing time-dependent behaviors and a saturation effect at high angular momentum.

## Contribution

It provides the first exact solutions for Dirac fermions in Aharonov-Bohm rings in a de Sitter expanding universe, highlighting relativistic effects and time dependence.

## Key findings

- Currents depend on time but relate as in non-relativistic cases.
- High angular momentum causes saturation of partial currents.
- Total persistent current evolves over time due to de Sitter expansion.

## Abstract

The $(1+3)$-dimensional Dirac equation of the fermions moving in ideal Aharonov-Bohm rings in the de Sitter expanding universe is used for deriving the exact expressions of the general relativistic partial currents and corresponding energies. In the de Sitter geometry, these quantities depend on time but these are related each other just as in the non-relativistic case or in special relativity. A specific relativistic effect is the saturation of the partial currents for high values of the total angular momentum. The total relativistic persistent current at $T=0$ takes over this property even though it is evolving in time because of the de Sitter expansion.