Zero-point fluctuations in the ground state of a mesoscopic normal ring - art. no. 165312

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 ma gnitude of the persistent current as a function of the external impedance i n the zero-temperature limit when the only fluctuations in the external cir cuit are zero-point fluctuations. These are time-dependent fluctuations tha t polarize the ring-dot structure and we discuss in detail the contribution of displacement currents to the persistent current. We have earlier discus sed 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 approac h is limited to weak coupling between the ring and the external circuit. We show that the zero-temperature persistent current obtained in this approac h is consistent with the persistent current calculated from the Bethe ansat z solution. In the absence of coupling our system is a two level system con sisting 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 s tate and the first exited state of the decoupled ring. With each of these p rojections we can associate a phase-diffusion time. In the zero-temperature limit We find that the phase-diffusion time of the excited state projectio n saturates, whereas the phase-diffusion time of the ground state projectio n diverges.