On the possibility of realizing a periodic low-density spatial distribution of excitons

The solutions of a system of coupled integro-differential Bogolyubov equations for distribution functions have been used to determine conditions, both in temperature and in concentration, under which a spatially uniform distribution of excitons transforms spontaneously into a periodic state with a small amplitude. The analysis rests on the concept assuming the existence of a biexciton interaction potential. The criterion for the appearance of a weak periodic component in the exciton distribution is derived from the condition of branching of solutions of Hammerstein-type equations at the point where the parameters of this equation reach critical values.