We investigate dissipative quantum transport in extended periodic syst
ems that are subjected to electric harmonic mixing fields E-hm(t) = E-
1 cos(Omega t) + E-2 cos(2 Omega t+phi) Although such a drive possesse
s no net bias on average, the interplay of quantum dissipation and non
linear response causes a finite directed current. We thus discover the
paradigm of a dissipative quantum rectifier. The quantum current exhi
bits multiple reversals when driven in the nonadiabatic regime. As a f
unction of temperature the quantum current displays a bell-shaped char
acteristic -constituting the benchmark for quantum stochastic resonanc
e. Moreover, harmonic mixing also serves as a novel tool to selectivel
y control quantum diffusion.