Persistent currents in metallic rings containing a quantum dot

•Langevin dynamics of the magnetic flux for classical and quantum Smoluchowski regimes.•Current-flux characteristics vs the amplitude and phase of the transmission coefficient.•Crucial role of the phase of the transmission coefficient.•Contribution to the development of effective control of current in mesoscopic rings.

Currents in metallic rings 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 modeled 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 current versus external magnetic flux. The type of response is more robust to changes of the amplitude of the transmission coefficient and more sensitive to changes of the phase around some values.