Quantum Transport and Quantum Pumping

The usual laws of the circuits (Ohm’s law, Kirchoff’s law, and so on) are valid in the macroscopic world. However, when the linear dimensions are less than an electron mean free path, which may be on the order of 10 nm (22 in Al and 55 in Cu), the motion of the electrons is ballistic, that is, the circuit obeys quantum laws.