Extension of the electrokinematics theorem to the electromagnetic field and quantum mechanics

Summary A recent electrokinematics theorem leads to a general equation that, through an arbitrary irrotational fieldF, connects the motion of the electric-charge carriers, the internal potential and the dielectric properties of a physical system with its external currents, voltages and powers. It has been proved for quasi-electrostatic fields,i.e. when the vector potential may be disregarded, and on the basis of classical mechanics. Here the theorem is extended to any type of electromagnetic field and to quasi-relativistic quantum mechanics, in the case of many-particle systems for which, moreover, the probability current density is suitably computed. The new equation so obtained, throughF, connects the external currents again with the internal electric permittivity and the scalar potential, in the same way as in the preceding approach, and with the carrier velocity that, however, has to be computed according to quantum mechanics. Moreover, it contains two new contributions, one deriving from the vector potential and the other from a current density arising from the electron spin. By means of proper choices ofF, new expressions of the external currents of the system are determined as functions of the motion of its internal carriers. In particular, the electrokinematics theorem is exploited to compute the output current in two-terminal nanoelectronic devices in which, owing to the small sizes, quantum effects cannot be disregarded. Finally, such results, when they are applied to the double-barrier tunnelling structures, allow us to show the splitting of the electron pulse into two uncorrelated pulses, and as a consequence, to obtain a possible shot noise suppression, up to fifty per cent of the full shot noise.