  The ground state of a phase-coherent mesoscopic system is sensitive to its
environment. We investigate the persistent current of a ring with a quantum dot
which is capacitively coupled to an external circuit with a dissipative
impedance. At zero temperature, zero-point quantum fluctuations lead to a
strong suppression of the persistent current with decreasing external
impedance. We emphasize the role of displacement currents in the dynamical
fluctuations of the persistent current and show that with decreasing external
impedance the fluctuations exceed the average persistent current.
