  As pointed out by Kutschera and W{\'o}jcik, very low concentration of protons
combined with a specific density dependence of effective neutron-proton
interaction could lead to a localization of ``proton impurities'' in neutron
medium at densities exceeding four times normal nuclear matter density. We
study consequences of the localization of protons for transport processes in
dense neutron star cores, assuming random distribution of proton impurities.
Kinetic equations, relevant for the transport of charge, heat and momentum, are
solved using variational method. Localization of protons removes a T^{-2}
factor from the transport coefficients, which leads, at lower temperatures, to
a strong decrease of thermal conductivity, electrical conductivity and shear
viscosity of neutron star matter, as compared to the standard case, where
protons form a Fermi liquid. Due to the localization of protons a number of
conventional neutrino emission processes (including modified URCA process)
become inoperative in neutron star cores. On the other hand, the energy loss
rate from neutrino-antineutrino pair bremsstrahlung due to electron and neutron
scattering off (localized) protons, will have a specific T^6 dependence, which
could modify the cooling of the neutron star core, as compared to the standard
case. Possible astrophysical implications of the localization of protons for
neutron star evolution and dynamics are discussed.
