  We examine the properties of atomic current in a superfluid oscillating
circuit consisting of a mesoscopic channel that connects two reservoirs of a
Bose-Einstein condensate. We investigate the presence of a critical current in
the channel and examine how the amplitude of the oscillations in the number
imbalance between the two reservoirs varies with system parameters. In addition
to highlighting that the dissipative resistance stems from the formation of
vortex pairs, we also illustrate the role of these vortex pairs as a quantum
current regulator. The dissipation strength is discrete based on the number
imbalance, which corresponds to the emergence of vortex pairs in the system.
Our findings indicate that the circuit demonstrates characteristics of both
voltage-limiting and current-limiting mechanisms. To model the damping behavior
of the atomic superfluid circuit, we develop an equivalent LC oscillator
circuit with a quantum current regulator.
