Concurrence Dynamics in Self-Gravitating Mixed Neutrinos

Abstract

We study the entanglement generated by Newtonian self-gravity in a two-particle system of mixed neutrinos and quantify it by means of the concurrence. Starting from the gravitational coupling between the mass operators, we show that the two-particle Hamiltonian splits into local single-particle terms and an effective Ising interaction in the mass basis, the latter being solely responsible for the generation of correlations. For initially separable flavor states the concurrence is obtained in closed analytic form: it oscillates between zero and a maximum fixed by the mixing angle alone, while the gravitational coupling sets the recurrence time. We further establish a one-to-one correspondence between the concurrence and the reduced-state purity previously derived for this model, thus providing an independent quantum-information description of the same gravitationally induced correlations. Finally, we show that the concurrence does not depend on the Majorana phase, so that Dirac and Majorana parametrizations yield identical entanglement dynamics. These results isolate the genuinely entangling sector of the gravitational evolution and provide a compact analytic characterization of gravity-induced quantum correlations in mixed neutrino systems.