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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2409.14841 |
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Table of Contents:
- We give a rigorous derivation of the Hartree equation for the many-body dynamics of pseudo-relativistic Fermi systems at high density $\varrho \gg 1$, on arbitrarily large domains, at zero temperature. With respect to previous works, we show that the many-body evolution can be approximated by the Hartree dynamics locally, proving convergence of the expectation of observables that are supported in regions with fixed volume, independent of $\varrho$. The result applies to initial data describing fermionic systems at equilibrium confined in arbitrarily large domains, under the assumption that a suitable local Weyl-type estimate holds true. The proof relies on the approximation of the initial data through positive temperature quasi-free states, that satisfy strong local semiclassical bounds, which play a key role in controlling the growth of the local excitations of the quasi-free state along the many-body dynamics.