Memory effects in adiabatic quantum pumping with parasitic nonlinear dynamics

The charge current adiabatically pumped through a mesoscopic region coupled to a classical variable obeying a nonlinear dynamics is studied within the scattering matrix approach. Due to the nonlinearity in the dynamics of the variable, a hysteretic behavior of the pumping current can be observed for specific characteristics of the pumping cycle. The steps needed to build a quantum pump working as a memory device are discussed together with a possible experimental implementation.