A study on quantum decoherence phenomena with three generations of neutrinos

Using the open quantum system approach applied to the neutrino system, we derive three generations neutrino probability formulae considering the oscillation induced by mass plus quantum decoherence contributions. The introduction of these dissipative effects is done through the quantum dynamical semigroup formalism. In addition to the theoretical interest of the approach, at least from the completeness point of view, this extension of the formalism to the three flavors, provide us with a direct application: we can analyze qualitatively the consistency of the two generation pure decoherence solution to the atmospheric neutrino problem, accommodated within this enlarged scheme, with the mean tendencies observed for some of the current neutrino experimental data. This study was performed based on different choices of the $3 \times 3$ mixing matrix selected in order to adjust the $P_{\nu_{\mu} \to \nu_{\mu}}$ to the same form it has for the decoherence solution in two generations. Our qualitative tests for decoherence with three neutrinos show a clear incompatibility between neutrino data and the theoretical expectations.