Polynomial method for canonical calculations

A practical version of the polynomial canonical formalism is developed for normal mesoscopic systems consisting of N noninteracting electrons. Drastic simplification of calculations is attained by means of a proper ordering of excited states of the system. It results in that the exact canonical partition function can be represented as a series in which the first term corresponds to the ground state whereas successive groups of terms belong to many particle–hole excitations (one particle–hole, two particle–hole and so on). The number of terms which should be taken into account weakly depends on N and does not exceed 2kBT/δF (δF is the mean level spacing near the Fermi level). The elaborated method is free from limitations on N and T and makes the canonical calculations practically not more complicated than the grand canonical ones.