Zero-point fluctuations in the ground state of a mesoscopic normal ring

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 that 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 the 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.