Statistics of hole pairs in a crystal lattice

Abstract

The system of coupled hole pairs in a crystal lattice is studied. The exact commutation relations for the hole pair operators correspond to a modified parafermi statistics of rank M ̄ ( M ̄ is the number of sites in a “superlattice” formed by centers of mass for each hole pair), i.e. one state can be occupied by up to M ̄ pairs. Even in the absence of dynamic interaction, the system of hole pairs is characterized by some immanent interaction (kinematic interaction). In spite of the kinematic interaction, there is no statistical prohibitions on the Bose–Einstein condensation of coupled hole pairs.