Randomly fluctuating potential-controlled multistable resonant tunneling current through a quantum dot

There is a long-standing controversy about the existence of more than one steady state in the transport through quantum dots and molecules. In this letter, we present a theory of the multiple steady states driven by randomly fluctuating potentials simulated by the autoregressive model. We find two general conditions under which the steady states strongly depend on the history of the fluctuating potential: First, the fluctuating potential has a nonzero correlation time. Second, it is applied before the steady states are built up under the decoupled initial condition. Furthermore, we provide a way of controlling the stationary current by the correlation time and strength of the fluctuation.