Two-time Green's functions and spectral density method in nonextensive quantum statistical mechanics

TL;DR

This paper extends the Green's functions and spectral density methods to nonextensive quantum statistical mechanics, enabling analysis of equilibrium and transport properties in systems with nonextensivity, exemplified by a high-density Bose gas.

Contribution

It introduces a formalism for two-time Green's functions and spectral density in nonextensive quantum systems, providing tools for studying nonextensivity effects in many-body physics.

Findings

Explicit calculation of thermodynamic quantities near the extensive regime

Application to a high-density Bose gas model with strong attraction

Demonstration of methods' effectiveness in nonextensive conditions

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 $q$-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.