Work

Effective Dynamics of Local Observables for Extended Fermi Gases in the High-Density Regime

Year: 2025

Type: article

Abstract: We give a rigorous derivation of the Hartree equation for the many-body dynamics of pseudo-relativistic Fermi systems at high density $$\varrho \gg 1$$ ϱ ≫ 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 $$\varrho $$ ϱ . 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.

Source: Communications in Mathematical Physics

DOI: 10.1007/s00220-025-05393-4

Authors: Luca Fresta, Marcello Porta, Benjamin Schlein

Institutions: University of Bonn, Hausdorff Center for Mathematics, Scuola Internazionale Superiore di Studi Avanzati, University of Zurich

Language: English

Topic: Advanced Mathematical Physics Problems

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $2,990