  We study dynamical (quasi)-condensation in the Fermi-Hubbard model starting
from a completely uncorrelated initial state of adjacent doubly occupied sites.
We show that upon expansion of the system in one dimension, dynamical
(quasi)-condensation occurs not only for large interactions via the
condensation of doublons, but also for small interactions. The behavior of the
system is distinctly different in the two parameter regimes, underlining a
different mechanism at work. We address the question whether the dynamical
(quasi-)condensation effect persists in the thermodynamic limit. For this
purpose, we use the two-particle reduced density matrix method, which allows
the extension to large system sizes, long propagation times, and
two-dimensional (2D) systems. Our results indicate that the effect vanishes in
the thermodynamic limit. However, especially in 2D, further investigation
beyond numerically tractable system sizes calls for the use of quantum
simulators, for which we show that the described effect can be investigated by
probing density fluctuations.
