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.