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Published on: May 27, 2020
Two-time Green's functions and spectral density method in nonextensive quantum statistical mechanics.
A Cavallo1, F Cosenza, L De Cesare
1Institut Charles Sadron, Campus CNRS Cronenbourg, 23 rue du Loess, BP 84047, 67034 Strasbourg Cedex 2, France.
Summary
This study extends thermodynamic Green's functions to nonextensive quantum statistics, introducing methods to calculate q-spectral properties and spectral densities for nonextensive systems. These methods reveal q-induced nonextensivity effects in Bose gases.
Area of Science:
- Quantum statistical mechanics
- Nonextensive thermodynamics
- Many-body physics
Background:
- Thermodynamic two-time Green's functions are crucial for analyzing quantum systems.
- Nonextensive statistical mechanics offers a framework for systems deviating from traditional statistical assumptions.
- Spectral density methods are effective for exploring equilibrium and transport properties.
Purpose of the Study:
- To extend the formalism of thermodynamic two-time Green's functions to nonextensive quantum statistical mechanics.
- To present methods for calculating two-time q-Green's functions and q-spectral densities.
- To investigate q-induced nonextensivity effects in a Bose gas model.
Main Methods:
- Utilizing the optimal Lagrangian multiplier representation.
- Developing direct calculation methods for two-time q-Green's functions and q-spectral density.
- Applying equations of motion and spectral density methods.
- Analyzing a second-quantized model for a high-density Bose gas with strong attraction.
Main Results:
- Presented methods for calculating q-spectral properties analogous to extensive systems (q=1).
- Emphasized the nonextensive spectral density method for studying complex systems.
- Explicitly calculated contributions of q-induced nonextensivity to thermodynamic quantities in a Bose gas model.
- Overcame challenges in calculating the q grand-partition function.
Conclusions:
- The developed methods effectively analyze q-induced nonextensivity in many-body systems.
- The study provides insights into the equilibrium properties of Bose gases under nonextensive conditions.
- The formalism offers a pathway to explore diverse physical phenomena in nonextensive quantum systems.
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