# High-frequency electromagnetic emission from non-local wavefunctions

## TL;DR

This paper explores the unique electromagnetic emissions resulting from non-local quantum currents, revealing long-range longitudinal fields that could impact nano-electronic and superconducting device applications.

## Contribution

It demonstrates that non-local quantum currents produce significant long-range longitudinal electromagnetic fields, extending understanding of quantum transport and electromagnetic interactions.

## Key findings

- Long-range longitudinal electric fields are generated by non-local currents.
- The longitudinal field can be 100-1000 times stronger than the transverse component.
- Potential applications include Josephson junctions and molecular nano-devices.

## Abstract

In systems with non-local potentials or other kinds of non-locality, the Landauer-B\"uttiker formula of quantum transport leads to replace the usual gauge-invariant current density $\textbf{J}$ with a current $\textbf{J}^{ext}$ 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 $\sim 10^{-7}$ 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 SNS junctions in YBCO and by current flow in molecular nano-devices.