  Gauge theories arise in physical systems displaying space-time local
symmetries. They provide a powerful description of important realms of physics
ranging from fundamental interactions, to statistical mechanics, condensed
matter and more recently quantum computation. As such, a remarkably deep
understanding has been achieved in the field. With the advent of quantum
technology, lower energy analogs, capable to capture important features of the
original quantum field theories through quantum simulation, have been
intensively studied. Here, we propose a specific scheme implementing an
analogic quantum simulation of lattice gauge theories constrained to mesoscopic
spatial scales. To this end, we study the dynamics of mesons residing in a
ring-shaped lattice of mesoscopic size pierced by an effective magnetic field.
In particular, we find a new type of Aharonov-Bohm effect that goes beyond the
particle-like effect and reflecting the the features of the confining gauge
potential. The coherence properties of the meson are quantified by the
persistent current and by specific features of the correlation functions. When
the magnetic field is quenched, Aharonov-Bohm oscillations and correlations
start a specific matter-wave current dynamics.
