Dynamics of mean-field Fermi systems with nonzero pairing
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866909329763860480 |
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| author | Marcantoni, Stefano Porta, Marcello Sabin, Julien |
| author_facet | Marcantoni, Stefano Porta, Marcello Sabin, Julien |
| contents | We study the dynamics of many-body Fermi systems, for a class of initial data which are close to quasi-free states exhibiting a nonvanishing pairing matrix. We focus on the mean-field scaling, which for fermionic systems is naturally coupled with a semiclassical scaling. Under the assumption that the initial datum enjoys a suitable semiclassical structure, we give a rigorous derivation of the time-dependent Hartree-Fock-Bogoliubov equation, a nonlinear effective evolution equation for the one-particle density matrix of the system, as the number of particles goes to infinity. Our result holds for all macroscopic times, and provides bounds for the rate of convergence. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_15280 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Dynamics of mean-field Fermi systems with nonzero pairing Marcantoni, Stefano Porta, Marcello Sabin, Julien Mathematical Physics We study the dynamics of many-body Fermi systems, for a class of initial data which are close to quasi-free states exhibiting a nonvanishing pairing matrix. We focus on the mean-field scaling, which for fermionic systems is naturally coupled with a semiclassical scaling. Under the assumption that the initial datum enjoys a suitable semiclassical structure, we give a rigorous derivation of the time-dependent Hartree-Fock-Bogoliubov equation, a nonlinear effective evolution equation for the one-particle density matrix of the system, as the number of particles goes to infinity. Our result holds for all macroscopic times, and provides bounds for the rate of convergence. |
| title | Dynamics of mean-field Fermi systems with nonzero pairing |
| topic | Mathematical Physics |
| url | https://arxiv.org/abs/2310.15280 |