Free Time Evolution of a Tracer Particle Coupled to a Fermi Gas in the High-Density Limit
Abstract
© 2017, Springer-Verlag GmbH Germany. The dynamics of a particle coupled to a dense
and homogeneous ideal Fermi gas in two spatial dimensions is studied. We analyze the
model for coupling parameter g = 1 (i.e., not in the weak coupling regime), and prove
closeness of the time evolution to an effective dynamics for large densities of the
gas and for long time scales of the order of some power of the density. The effective
dynamics is generated by the free Hamiltonian with a large but constant energy shift
which is given at leading order by the spatially homogeneous mean field potential
of the gas particles. Here, the mean field approximation turns out to be accurate
although the fluctuations of the potential around its mean value can be arbitrarily
large. Our result is in contrast to a dense bosonic gas in which the free motion of
a tracer particle would be disturbed already on a very short time scale. The proof
is based on the use of strong phase cancellations in the deviations of the microscopic
dynamics from the mean field time evolution.
Type
Journal articlePermalink
https://hdl.handle.net/10161/17107Published Version (Please cite this version)
10.1007/s00220-017-2970-2Publication Info
Jeblick, M; Mitrouskas, D; Petrat, S; & Pickl, P (2017). Free Time Evolution of a Tracer Particle Coupled to a Fermi Gas in the High-Density
Limit. Communications in Mathematical Physics, 356(1). 10.1007/s00220-017-2970-2. Retrieved from https://hdl.handle.net/10161/17107.This is constructed from limited available data and may be imprecise. To cite this
article, please review & use the official citation provided by the journal.
Collections
More Info
Show full item recordScholars@Duke
Peter Pickl
Visiting Professor of Global Studies
Starting with the autumn term 2018 I will teach the foundational mathematics and integrated
science courses in the undergraduate program at DKU. In the coming years, other classes
on several topics of mathematics and mathematical physics will be taught.

Articles written by Duke faculty are made available through the campus open access policy. For more information see: Duke Open Access Policy
Rights for Collection: Scholarly Articles
Works are deposited here by their authors, and represent their research and opinions, not that of Duke University. Some materials and descriptions may include offensive content. More info