  Dynamical mean field theory (DMFT) is used to study neutron matter, both with
and without admixture of the proton fraction. The system is approximated by the
lattice Habbard model. The corresponding equation of state as a function of
temperature/density/asymmetry is investigated. The results are compared with
the standard mean field (MF) approach where the effect of local correlations is
neglected. Whereas the influence of the correlations on the properties of a
pure neutron matter is found to be moderate, it becomes strong when the proton
admixture is taken into account. In particular, we calculate the proton
fraction, energy density and pressure in outer core of neutron stars, taking
into account the beta equilibrium condition. The DMFT predicts that the proton
fraction is several times the MF based calculations, whereas the DMFT results
for energy density and pressure are 30-40\% lower then the corresponding MF
estimates. Physical implications of our findings for a neutron star dynamics
are discussed.
