Quantum coherence of the ground state of a mesoscopic ring

We discuss the phase coherence properties of a mesoscopic normal ring coupl ed to an electric environment via Coulomb interactions. This system can be mapped onto the Caldeira-Leggett model with a flux dependent tunneling ampl itude. We show that depending on the strength of the coupling between the r ing and the environment the free energy can be obtained either by a Bethe a nsatz approch (for weak coupling) or by using a perturbative expression whi ch we derive here (in the case of strong coupling). We demonstrate that the zero-point fluctuations of the environment can strongly suppress the persi stent current of the ring below its value in the absence of the environment . This is an indication that the equilibrium fluctuations in the environmen t disturb the coherence of the wave functions in the ring. Moreover the inf luence of quantum fluctuations can induce symmetry breaking seen in the pol arization of the ring and in the flux induced capacitance. (C) 2001 Academi c Press.