Electromagnetic Signatures of Possible Charge Anomalies in Tunneling

Abstract

We reconsider some well-known tunneling processes from the point of view of Aharonov-Bohm electrodynamics, a unique extension of Maxwell’s theory which admits charge-current sources that are not locally conserved. In particular we are interested into tunneling phenomena having relatively long range (otherwise the non-Maxwellian effects become irrelevant, especially at high frequency) and involving macroscopic wavefunctions and coherent matter, for which it makes sense to evaluate the classical e.m. field generated by the tunneling particles. For some condensed-matter systems, admitting discontinuities in the probability current is a possible way of formulating phenomenological models. In such cases, the Aharonov-Bohm theory offers a logically consistent approach and allows to derive observable consequences. Typical e.m. signatures of the failure of local conservation are at high frequency the generation of a longitudinal electric radiation field, and at low frequency a small effect of “missing” magnetic field. Possible causes of this failure are instant tunneling and phase slips in superconductors. For macroscopic quantum systems in which the phase-number uncertainty relation ΔNΔφ∼1 applies, the expectation value of the anomalous source I=∂tρ+∇·j has quantum fluctuations, thus becoming a random source of weak non-Maxwellian fields.

Simple circuit and experimental proposal for the detection of gauge-waves

“…While no generally accepted explanation of these superconductive properties exists, it is quite clear that conduction in graphite involves effects of macroscopic quantization. In this case one may expect some violations of local charge conservation because (1) several phenomenological non-BCS models of superconductivity comprise nonlocal wave equations [18]; (2) the number/phase uncertainty relation ΔNΔf ; 1 and the non-commutativity of the quantum operators r ˆand j împoses a quantum uncertainty on the operator r ¶ +  j t ˆ•ˆ [ 17].…”

“…The extended theory of electrodynamics by Aharonov and Bohm [2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19] is a generalization of the familiar Maxwell theory which allows to couple the e.m. field also to sources where charge is not locally conserved-a phenomenon that is expected to occur in certain physical system with meso-or macroscopic quantum effects. Just because of this more general setting, the theory is not gauge invariant, and the electric and magnetic potentials f, A become univocally defined.…”

“…Although the S field has been called 'auxiliary', because it is defined in terms of the potentials, it can manifest itself in principle in some small observable effects. Among these are waves with a longitudinal electric component and static currents with a partially 'missing' B [18,20]. The most relevant new physical effect predicted by the theory, however, is the possibility to detect pure gauge waves.…”

Aharonov–Bohm Electrodynamics in Material Media: A Scalar e.m. Field Cannot Cause Dissipation in a Medium

“…The only possible longitudinal mode transmitted is a gauge wave, as shown by the second equation in each of relations (20) and (21).…”

“…This extension is quite natural and was actually introduced with various motivations and technical approaches, even before the work by Aharonov and Bohm [1][2][3][4][5][6][7][8]. For recent reviews and developments, see [9][10][11][12][13][14][15][16][17][18][19][20][21].…”