Quantum collision current in electronic circuits.

Novel effects and phenomena that are not found at macroscopic length scales characterize the behavior of matter at the nanoscale. Electronic transport is a prominent example. When the spatial dimensions of a device are of the order of the electron wavelength, special features appear such as quantized conductance and ballistic transport. These phenomena are at the basis of molecular electronics and have been widely discussed in the literature. Here, we shall focus on a different and not as well-known quantum feature of electronic circuits. When a circuit of length L is described within classical or semiclassical approximations, the power needed for the circulation of a dc current I is given by W= LI in terms of the applied dc electromotive force . We will argue below that a larger power W> LI is required to circulate a current I in a quantum device. The reason for the inequality is that, in addition to the power needed to circulate the current I, some dc power is also needed to maintain a stationary charge distribution in the circuit. This is a genuine quantum effect. In circuits governed by the laws of classical physics, some power is needed to displace charges in the initial transient, but no dc power is required to maintain a stationary charge distribution when a dc current is flowing. To deal quantum mechanically with an electronic circuit, we consider a system of carriers (electrons) subjected to an applied electromotive force and coupled to a thermal reservoir held at constant temperature T. Dissipative effects, that is, inelastic scattering with the phonon modes of the reservoir, are necessary to maintain steady state and to prevent the electrons from accelerating indefinitely under the applied electromotive force. Under weak coupling conditions and if the timescale of inelastic scattering is much shorter than the current relaxation time, the reduced dynamics of the electrons is well approximated by a master Equation (1). 4]