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We study the transport through a quantum dot subject to a randomlyfluctuating potential, generated by a sequence of pulses in the gate voltagewith the help of the autoregressive model. We find that the tunneling currentis multistable when the fluctuating potential with a finite correlation time isapplied before the non-equilibrium steady state is built up. Thenon-equilibrium stationary current is heavily dependent on the history of thefluctuating potential during the transient period if the potential has a finitecorrelation time. Furthermore, the averaged current over the path of thefluctuating potential is a function of its strength and correlation time. Ourwork therefore provides a robust theoretical proposal for the controlling ofthe non-equilibrium stationary current through a quantum dot in a randomlyfluctuating potential.

Randomly Fluctuating Potential Controlled Multistable Resonant Tunneling Current through a Quantum Dot