Necessary and sufficient condition for quantum adiabaticity in a driven one-dimensional impurity-fluid system

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 $1\mathrm{/}N$ or faster. This improves the necessary adiabatic condition $F_N=O(1\mathrm{/}\log N)$ 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.