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We develop a nonadiabatic perturbation theory for oscillations involving an arbitrary number of neutrino and antineutrino species, including the possibility of lepton-number violation which we treat as a small effect. We interpret the physics of such an approach for the one generation case by introducing the notion of adiabaticity for neutrino and antineutrino oscillations in analogy to flavor oscillations. We find that in a CF-odd matter environment a small lepton-number violation in vacuo can be enhanced. Eventually, we apply the perturbation theory to the two generation case and work out an example for manifestations of lepton-number violation, which can be solved both perturbatively as well as analytically thereby further clarifying the nature of the perturbation expansion. [ABSTRACT FROM AUTHOR]

The standard wave function approach for the treatment of neutrino oscillations fails in situations where quantum ensembles at a finite temperature with or without an interacting background plasma are encountered. As a first step to treat such phenomena in a novel way, we propose a unified approach to both adiabatic and nonadiabatic two-flavor oscillations in neutrino ensembles with finite temperature and generic (e.g., matter) potentials. Neglecting effects of ensemble decoherence for now, we study the evolution of a neutrino ensemble governed by the associated quantum kinetic equations, which apply to systems with finite temperature. The quantum kinetic equations are solved formally using the Magnus expansion and it is shown that a convenient choice of the quantum mechanical picture (e.g., the interaction picture) reveals suitable parameters to characterize the physics of the underlying system (e.g., an effective oscillation length). It is understood that this method also provides a promising starting point for the treatment of the more general case in which decoherence is taken into account. [ABSTRACT FROM AUTHOR]