Distribution of charge carriers in a system of large radius polarons and bipolarons and delocalized carriers

Statistical properties of polarons and bipolarons of large radius have not been studied yet with the limitations of their momentums imposed by the spatial dispersion of ionic polarizability taken into account. We derive a distribution function for charge carriers in systems where autolocalized and delocalized carriers can occur. Properties of such a distribution turn out to be unusual. It shows that the concentration of polarons in the system is limited and the temperature region where they can occur is restricted from the top. The chemical potential in the system of autolocalized fermions and bosons and delocalized fermions can increase with the temperature, which makes possible bipolaron Bose-condensation, even if the bipolaron is not in the most energetically profitable state. A phase diagram Bose-vapour—Bose-condensate is constructed with the limitation on momentums of bipolarons allowed for. It shows, that owing to a sharp decrease in the number of states in the Bose-vapour of bipolarons caused by the momentum limitation, the temperature of the bipolaron Bose-condensation can attain 100-200K at typical values of the bipolaron effective mass.