Green functions based on Tsallis nonextensive statistical mechanics: normalized q-expectation value formulation

In this paper, the Green function theory of quantum many-particle systems r ecently presented is reworked within the framework of nonextensive statisti cal mechanics with a new normalized q-expectation values. This reformulatio n introduces a renormalization of temperature of the earlier theory and a s elf-consistency condition. The importance of these two features is nontrivi al and to emphasize this, we explicitly contrast the maximum entropy densit y matrices derived for an exactly solvable model based on the two types of the constraints. The linear response theory is also presented, along with i ts two-particle Green function version. In order to emphasize the importanc e of the new formalism, we collect here the results where both the formalis ms have been used to examine the same set of problems. This reveals clearly that the new formalism is the method of choice because the numerical resul ts are much more physically meaningful than those found in the old version, even though the general features or the answers retain the same characteri stics in certain cases. In the case where thermodynamic entities are to be examined as in the case of the q-dependence of Bose-Einstein condensation, the self-consistent requirement in the new formalism is numerically much mo re subtle, and thus the earlier results are modified as shown in Fig. 1. (C ) 2000 Elsevier Science B.V. All rights reserved.