  We search for marginal Fermi-liquid behavior in the two-band Hubbard model
with one narrow band. We consider the limit of low electron densities in the
bands and strong intraband and interband Hubbard interactions. We analyze the
influence of electron polaron effect and other mechanisms of mass-enhancement
(related to momentum dependence of the self-energies) on effective mass and
scattering times of light and heavy components in the clean case (electron -
electron scattering and no impurities). We find the tendency towards
phase-separation (towards negative partial compressibility of heavy particles)
in a 3D case for large mismatch between the densities of heavy and light bands
in a strong coupling limit. We also observe that for low temperatures and equal
densities the resistivity in a homogeneous state R(T) ~ T^2 - behaves in a
Fermi-liquid fashion both in 3D and 2D cases. For temperatures higher then
effective bandwidth for heavy electrons T > Wh* the coherent behavior of heavy
component is totally destroyed. The heavy particles move diffusively in the
surrounding of light particles. At the same time the light particles scatter on
the heavy ones as if on immobile (static) impurities. In this regime the heavy
component is marginal, while the light one is not. The resistivity goes on
saturation for T > Wh* in the 3D case. In 2D the resistivity has a maximum and
localization tail due to weak - localization corrections of Altshuler - Aronov
type. Such behavior of resistivity in 3D could be relevant for some
uranium-based heavy-fermion compounds like UNi2Al3 and in 2D for some other
mixed-valence compounds possibly including the layered manganites. We also
consider briefly the superconductive (SC) instability in the model. The leading
instability is towards p-wave pairing and is governed by enhanced Kohn -
Luttinger mechanism of SC at low electron density.
