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

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 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.

The effect of collisions with the wall on neutron-antineutron transitions

“…We note in passing that inside nuclei or in nuclear matter for relevant times Γt ≫ 1(Γ ∼ 10 23 s −1 ) equation (26) leads to a result which looks quaite different [6,26]…”

“…In the correct equations the waves hitting the wall and reflected from it must be mixtures of the n andn components. For the conversion inside nuclei coupled equations have been formulated and solved using either the optical potential [20,[22][23][24][25] or the Bloch equations [6]. To our knowledge Ref.…”

“…A commonplace is to treat this effect in terms of the Fermi potential (see [4] and references there in ). This approach is highly objectionable since in experiments with thermal neutrons and even with UCN the neutron wavelength is much smaller than the average intermolecular distance of the residual gas [6]. The neutron "can see" the individual gas molecules which rules out the use of Fermi potential.…”

“…As a result the " quantum friction" caused by the interaction with the environment leads to a drastic modification of the nn conversion law. The possible nn transition process proceeds in the overdamping instead of the oscilation regime -see [6] for a detailed description.…”

Quantum correlations and the neutrino mass degeneracy problem

“…The quantum correlations have been studied mainly in the optical and electronic systems [7][8][9][10]. Recently such studies have been extended to high energy physics owing to the advancement in various experimental facilities, see for example [11][12][13][14][15][16][17][18][19][20][21][22][23][24]. The concept of single particle entanglement has been introduced in previous studies [25][26][27] which have also been demonstrated experimentally with single photon systems [28][29][30].…”