Statistics and properties of coupled hole pairs in superconducting ceramics

It is shown that in site representation the hole-pair operators obey the sa me commutation relations (paulionic) as the Cooper pair operators in impuls e representation, although the latter describe delocalized quasiparticles. In quasi-impulse representation the hole-pair operators are also delocalize d but the exact commutation relations correspond to a modified parafermi st atistics [1] of rank N (N is the number of sites in a "superlattice" formed by the centers of mass of each hole pair). From this follows that one stat e can be occupied by up to N pairs. Even in the absence of dynamic interact ion, the system of hole pairs is characterized by some immanent interaction , named after Dyson as kinematic interaction. This interaction appears beca use of the deviation of the quasiparticle statistics from the Bose (Fermi) statistics and its magnitude depends on the concentration of hole pairs. In spite of the non-bosonic behavior, there is no statistical prohibition on the Bose-Einstein condensation of coupled hole pairs.