Quantum inductive circuits under ac and dc fields: Current manifestations of charge discreteness

It is well known that the electrical current of a quantum inductive circuits with charge discreteness qe displays Bloch-like oscillations (frequency ωB=qeεd-bar ) under a dc external voltage (εd). Here we consider the effect of a superposed ac voltage in the circuit. Resonances are explicitly found. In the limit of small external frequency (ω-bar ωB), the electrical (one-period-averaged) current exist and has always the same sign. This gives us an experimental method to measure discrete charge effects in (quantum) nanometric circuits since the established current is depending on charge discreteness