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

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 nn¯ 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 nn¯ conversion. We show that in all three cases decoherence due to the interaction with the environment leads to non-oscillatory evolution.