title: Two-time Green's functions and spectral density method in nonextensive quantum statistical mechanics.
abstract: We extend the formalism of the thermodynamic two-time Green's functions to nonextensive quantum statistical mechanics. Working in the optimal Lagrangian multiplier representation, the q -spectral properties and the methods for a direct calculation of the two-time q Green's functions and the related q -spectral density ( q measures the nonextensivity degree) for two generic operators are presented in strict analogy with the extensive (q=1) counterpart. Some emphasis is devoted to the nonextensive version of the less known spectral density method whose effectiveness in exploring equilibrium and transport properties of a wide variety of systems has been well established in conventional classical and quantum many-body physics. To check how both the equations of motion and the spectral density methods work to study the q -induced nonextensivity effects in nontrivial many-body problems, we focus on the equilibrium properties of a second-quantized model for a high-density Bose gas with strong attraction between particles for which exact results exist in extensive conditions. Remarkably, the contributions to several thermodynamic quantities of the q -induced nonextensivity close to the extensive regime are explicitly calculated in the low-temperature regime by overcoming the calculation of the q grand-partition function.
authors.affiliation: Institut Charles Sadron, Campus CNRS Cronenbourg, 23 rue du Loess, BP 84047, 67034 Strasbourg Cedex 2, France.
authors.forename: A
authors.initials: A
authors.lastname: Cavallo
authors.forename: F
authors.initials: F
authors.lastname: Cosenza
authors.forename: L
authors.initials: L
authors.lastname: De Cesare