The rescaled Schrödinger dynamics of N dense fermions with C^2 pair interactions converges to the time-dependent Hartree dynamics with explicit rate N^{-1/24}.
The quantitative semi-classical limit of a large Fermi system at zero temperature
1 Pith paper cite this work. Polarity classification is still indexing.
1
Pith paper citing it
abstract
In this article we consider a large system of fermions in a combined mean-field and semiclassical limit, in three dimensions. We investigate the convergence of the Wigner function of the ground state, towards the classical Thomas-Fermi theory. The main novelty of the present article is quantifying the convergence rate with respect to the semi-classical parameter. One of the main ingredients is a recent result on the validity of semi-classical commutator estimates satisfied by the Hartree theory. Singular potentials, up to the Coulomb interaction, are included.
citation-role summary
background 1
citation-polarity summary
fields
math-ph 1years
2025 1verdicts
CONDITIONAL 1roles
background 1polarities
unclear 1representative citing papers
citing papers explorer
-
Derivation of the time-dependent Hartree equations for strongly interacting dense fermionic systems
The rescaled Schrödinger dynamics of N dense fermions with C^2 pair interactions converges to the time-dependent Hartree dynamics with explicit rate N^{-1/24}.