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

TL;DR

This paper establishes a refined necessary condition for maintaining quantum adiabaticity in a one-dimensional impurity-fluid system, showing the external force must decrease at least as fast as 1/N with system size, improving previous bounds.

Contribution

The authors derive a new necessary condition for quantum adiabaticity in a driven 1D impurity-fluid system, demonstrating the force must vanish as 1/N or faster, refining earlier results.

Findings

Adiabatic fidelity depends on external force scaling with system size.

Force must decrease as 1/N or faster to maintain adiabaticity in large systems.

Improves previous condition of force scaling as 1/log N.

Abstract

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.