---
res:
bibo_abstract:
- We introduce a new method for deriving the time-dependent Hartree or Hartree-Fock
equations as an effective mean-field dynamics from the microscopic Schrödinger
equation for fermionic many-particle systems in quantum mechanics. The method
is an adaption of the method used in Pickl (Lett. Math. Phys. 97 (2) 151–164 2011)
for bosonic systems to fermionic systems. It is based on a Gronwall type estimate
for a suitable measure of distance between the microscopic solution and an antisymmetrized
product state. We use this method to treat a new mean-field limit for fermions
with long-range interactions in a large volume. Some of our results hold for singular
attractive or repulsive interactions. We can also treat Coulomb interaction assuming
either a mild singularity cutoff or certain regularity conditions on the solutions
to the Hartree(-Fock) equations. In the considered limit, the kinetic and interaction
energy are of the same order, while the average force is subleading. For some
interactions, we prove that the Hartree(-Fock) dynamics is a more accurate approximation
than a simpler dynamics that one would expect from the subleading force. With
our method we also treat the mean-field limit coupled to a semiclassical limit,
which was discussed in the literature before, and we recover some of the previous
results. All results hold for initial data close (but not necessarily equal) to
antisymmetrized product states and we always provide explicit rates of convergence.@eng
bibo_authorlist:
- foaf_Person:
foaf_givenName: Sören P
foaf_name: Petrat, Sören P
foaf_surname: Petrat
foaf_workInfoHomepage: http://www.librecat.org/personId=40AC02DC-F248-11E8-B48F-1D18A9856A87
orcid: 0000-0002-9166-5889
- foaf_Person:
foaf_givenName: Peter
foaf_name: Pickl, Peter
foaf_surname: Pickl
bibo_doi: 10.1007/s11040-016-9204-2
bibo_issue: '1'
bibo_volume: 19
dct_date: 2016^xs_gYear
dct_language: eng
dct_publisher: Springer@
dct_title: A new method and a new scaling for deriving fermionic mean-field dynamics@
...