Within the framework of the two-Higgs Doublet Model (2HDM), we attempt to find some discrete, non-abelian flavour symmetry which could provide an explanation for the masses and mixing matrix elements of leptons. Unlike the Standard Model, currently there is no need for the flavour symmetry to be broken. With the GAP program we investigate all finite subgroups of the U3 group up to the order of 1025. Up to such an order there is no group for which it is possible to select free model parameters in order to match the masses of charged leptons, masses of neutrinos, and the Pontecorvo-Maki-Nakagawa-Sakata mixing matrix elements in a satisfactory manner.

The K3 quantity, introduced in a context of the Leggett-Garg inequality violation, is studied for the neutrino oscillations in matter with phenomenologically modelled dissipative environment. It is shown that the K3 function acquires different values depending on whether neutrino is Dirac or Majorana particle, provided that there is a dissipative interaction between matter and neutrinos. The difference occurs for various matter densities and can serve as a potential quantifier verifying the neutrino nature. Moreover, working within phenomenological model one can suggest the values of the matter density and dissipation for which the difference is the most visible. There exist also special conditions in which the violation of the Leggett-Garg inequality, to a different extent for both kinds of neutrino, is observed.

Even the subtle and apparently strange quantum effects can sometimes survive otherwise lethal influence of an omnipresent decoherence. We show that an archetypal quantum Cheshire Cat, a paradox of a separation between a position of a quantum particle, a photon, and its internal property, the polarization, in a two-path Mach–Zehnder setting, is robust to decoherence caused by a bosonic infinite bath locally coupled to the polarization of a photon. Decoherence affects either the cat or its grin depending on which of the two paths is noisy. For a pure decoherence, in an absence of photon–environment energy exchange, we provide exact results for weak values of the photon position and polarization indicating that the information loss affects the quantum Cheshire Cat only qualitatively and the paradox survives. We show that it is also the case beyond the pure decoherence for a small rate of dissipation.