Effect of relevant umklapp process on the two-leg Hubbard ladder with a half-filled band under pressure

By using integral representations the perturbation expansion and the Bogoliubov inequality ain nonextensive Tsallis statistics are investigated in a unified way. This procedure extends the analysis performed recently by Lenzi et al. [Phys. Rev. Lett. 80, 218 (1998)] to the quantum (discrete spectra) case, for q < 1. An example is presented in order to illustrate the method.