We investigate the persistent current of a ring with an in-line quantum dot
capacitively coupled to an external circuit. Of special interest is the
magnitude of the persistent current as a function of the external impedance in
the zero temperature limit when the only fluctuations in the external circuit
are zero-point fluctuations. These are time-dependent fluctuations which
polarize the ring-dot structure and we discuss in detail the contribution of
displacement currents to the persistent current. We have earlier discussed an
exact solution for the persistent current and its fluctuations based on a Bethe
ansatz. In this work, we emphasize a physically more intuitive approach using a
Langevin description of the external circuit. This approach is limited to weak
coupling between the ring and the external circuit. We show that the zero
temperature persistent current obtained in this approach is consistent with the
persistent current calculated from a Bethe ansatz solution. In the absence of
coupling our system is a two level system consisting of the ground state and
the first excited state. In the presence of coupling we investigate the
projection of the actual state on the ground state and the first exited state
of the decoupled ring. With each of these projections we can associate a phase
diffusion time. In the zero temperature limit we find that the phase diffusion
time of the excited state projection saturates, whereas the phase diffusion
time of the ground state projection diverges.Comment: 12 pages, 5 figure
