Abstract
In systems with non-local potentials or other kinds of non-locality, the Landauer-Büttiker formula of quantum transport leads to replacing the usual gauge-invariant current density J with a current J e x t which has a non-local part and coincides with the current of the extended Aharonov-Bohm electrodynamics. It follows that the electromagnetic field generated by this current can have some peculiar properties and in particular the electric field of an oscillating dipole can have a long-range longitudinal component. The calculation is complex because it requires the evaluation of double-retarded integrals. We report the outcome of some numerical integrations with specific parameters for the source: dipole length ∼10−7 cm, frequency 10 GHz. The resulting longitudinal field E L turns out to be of the order of 10 2 to 10 3 times larger than the transverse component (only for the non-local part of the current). Possible applications concern the radiation field generated by Josephson tunnelling in thick superconductor-normal-superconductor (SNS) junctions in yttrium barium oxide (YBCO) and by current flow in molecular nanodevices.
Highlights
The extended Maxwell equations by Aharonov and Bohm [1,2,3,4,5,6,7,8,9,10] are employed for the calculation of electromagnetic fields generated by sources which violate the local charge conservation condition∂t ρ + ∇ · J = 0
Barring exceptional situations in cosmology where such violations may occur at the macroscopic level, a possible microscopic failure of local conservation has been predicted in quantum mechanics in the following situations: 1
In systems described by fractional quantum mechanics [11,12,13,14,15,16,17]
Summary
The extended Maxwell equations by Aharonov and Bohm [1,2,3,4,5,6,7,8,9,10] are employed for the calculation of electromagnetic fields generated by sources which violate the local charge conservation condition. The authors of [27] prove that the current calculated from the surface integral of Jext over the interface between the scattering region and the lead α is equal to the that obtained from Equation (9) For this purpose, they express Jext in terms of Green functions, generalizing the standard method of [32] to the case of a non-local potential. The paper is organized as follows: In Section 2 we first recall a formal argument showing that the extended equations in vacuum can have solutions with a longitudinal propagating component; we define the non-conserved dipolar source used for the numerical calculation and we list the formal steps necessary for computing the electric field and we illustrate the method followed in the Monte.
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