# Lindblad and Bloch equations for conversion of a neutron into an antineutron

## TL;DR

This paper introduces a novel approach using Lindblad and Bloch equations to model neutron-antineutron conversion, highlighting the role of environmental decoherence in different experimental scenarios.

## Contribution

It applies density matrix formalism to neutron-antineutron oscillations, distinguishing between oscillatory and non-oscillatory conversions under environmental decoherence effects.

## Key findings

- Decoherence causes non-oscillatory evolution in all three experimental strategies.
- The probability of neutron to antineutron conversion depends on the environment and interaction details.
- Different experimental setups exhibit distinct dynamical behaviors due to decoherence effects.

## Abstract

We propose a new approach based on the Lindblad and Bloch equations for the density matrix to the problem of a neutron into an antineutron conversion. We consider three strategies to search for conversion: experiments with trapped neutrons, oscillations in nuclei, and quasi-free propagation. We draw a distinction between $n\bar{n}$ oscillations in which the probability that a neutron transforms into an antineutron depends on time according to the sine-square law and the non-oscillatory overdamped $n\bar{n}$ conversion. We show that in all three cases decoherence due to the interaction with the environment leads to non-oscillatory evolution.