  We study under what conditions the quantum adiabaticity is maintained in a
closed many-body system consisting of a one-dimensional fluid and an impurity
particle dragged through the latter by an external force. We employ an
effective theory describing the low-energy sector of the system to derive the
time dependence of the adiabaticity figure of merit -- the adiabatic fidelity.
We find that in order to maintain adiabaticity in a large system the external
force, $F_N$, should vanish with the system size, $N$, as $1/N$ or faster. This
improves the necessary adiabatic condition $F_N=O(1/\log N)$ obtained for this
system earlier [AIP Conf. Proc. 1936, 020024 (2018)]. Experimental implications
of this result and its relation to the quasi-Bloch oscillations of the impurity
are discussed.
