Currents in metallic rings with quantum dot

Currents in a metallic ring with a quantum dot are studied in the framework of a Langevin equation for a magnetic flux passing through the ring. Two scenarios are considered: one in which thermal fluctuations of the dissipative part of the current are modelled by classical Johnson-Nyquist noise and one in which quantum character of thermal fluctuations is taken into account in terms of a quantum Smoluchowski equation. The impact of the amplitude and phase of the transmission coefficient of the electron through a quantum dot on current characteristics is analyzed. In tailored parameter regimes, both scenarios can exhibit the transition from para-- to diamagnetic response of the ring current versus external magnetic flux.