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Abstract

Neutrino flavour transmutations in nonuniform matter are described by a
Schr\"{o}dinger-like evolution equation with coordinate-dependent potential. In
all the derivations of this equation it is assumed that the potential, which is
due to coherent forward scattering of neutrinos on matter constituents, is a
continuous function of coordinate that changes slowly over the distances of the
order of the neutrino de Broglie wavelength. This tacitly assumes that some
averaging of the microscopic potential (which takes into account the discrete
nature of the scatterers) has been performed.The averaging, however, must be
applied to the microscopic evolution equation as a whole and not just to the
potential. Such an averaging has never been explicitly carried out. We fill
this gap by considering the transition from the microscopic to macroscopic
neutrino evolution equation through a proper averaging procedure. We discuss
some subtleties related to this procedure and establish the applicability
domain of the standard macroscopic evolution equation. This, in particular,
allows us to answer the question of when neutrino propagation in rarefied media
(such as e.g.\ low-density gases or interstellar or intergalactic media) can be
considered within the standard theory of neutrino flavour evolution in matter.