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Dynamics of Mean-Field Fermi Systems with Nonzero Pairing
Stefano Marcantoni1, Marcello Porta2, Julien Sabin3
1Université Côte d'Azur Parc Valrose, 06108 Nice, France.
Annales Henri Poincare
|August 4, 2025
Summary
This study rigorously derives the time-dependent Hartree-Fock-Bogoliubov equation for many-body Fermi systems. The findings apply to systems with nonvanishing pairing, offering insights into their long-term dynamics.
Area of Science:
- Quantum mechanics
- Condensed matter physics
- Statistical mechanics
Background:
- Many-body Fermi systems are complex to model, especially those with pairing.
- Understanding their dynamics under mean-field and semiclassical scaling is crucial.
Purpose of the Study:
- To rigorously derive the time-dependent Hartree-Fock-Bogoliubov (TDHFB) equation for Fermi systems.
- To analyze the dynamics of systems near quasi-free states with nonvanishing pairing.
- To establish the validity of the derived equation for macroscopic times.
Main Methods:
- Focusing on mean-field and semiclassical scaling.
- Assuming initial data with a suitable semiclassical structure.
- Deriving the nonlinear effective evolution equation for the generalized one-particle density matrix.
Main Results:
- Rigorous derivation of the time-dependent Hartree-Fock-Bogoliubov equation.
- The equation governs the dynamics of the generalized one-particle density matrix.
- The derivation holds for all macroscopic times.
Conclusions:
- The TDHFB equation provides an accurate description of many-body Fermi systems with pairing.
- The study establishes theoretical bounds for the rate of convergence.
- This work advances the understanding of quantum many-body dynamics.
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