Two-time Green's functions and spectral density method in nonextensive quantum statistical mechanics
arXiv:0710.5695 · doi:10.1103/PhysRevE.77.051110
Abstract
We extend the formalism of the thermodynamic two-time Green's functions to nonextensive quantum statistical mechanics. Working in the optimal Lagrangian multipliers representation, the -spectral properties and the methods for a direct calculation of the two-time % -Green's functions and the related -spectral density ( measures the nonextensivity degree) for two generic operators are presented in strict analogy with the extensive () 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 -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 -induced nonextensivity close to the extensive regime are explicitly calculated in the low-temperature regime by overcoming the calculation of the grand-partition function.
48 pages, no figures
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