Quantum Coherence of the Ground State of a Mesoscopic Ring

We discuss the phase coherence properties of a mesoscopic normal ring coupled to an electric environment via Coulomb interactions. This system can be mapped onto the Caldeira-Leggett model with a flux dependent tunneling amplitude. We show that depending on the strength of the coupling between the ring and the environment the free energy can be obtained either by a Bethe ansatz approch (for weak coupling) or by using a perturbative expression which we derive here (in the case of strong coupling). We demonstrate that the zero-point fluctuations of the environment can strongly suppress the persistent current of the ring below its value in the absence of the environment. This is an indication that the equilibrium fluctuations in the environment disturb the coherence of the wave functions in the ring. Moreover the influence of quantum fluctuations can induce symmetry breaking seen in the polarization of the ring and in the flux induced capacitance.