# Design of a test for the electromagnetic coupling of non-local wavefunctions

## TL;DR

This paper proposes a test for detecting anomalous magnetic fields caused by non-local wavefunctions in fractional quantum mechanics, with potential experimental detection in cuprate superconductors.

## Contribution

It introduces a concrete experimental framework to detect non-local electromagnetic effects in quantum systems, extending Maxwell's equations for specific condensed matter scenarios.

## Key findings

- Anomalous magnetic fields are detectable with sensitive experiments.
- The spatial dependence and amplitude of the fields depend on microscopic parameters.
- Virtual charge effects are significant at the microscopic level.

## Abstract

It has recently been proven that certain effective wavefunctions in fractional quantum mechanics and condensed matter do not have a locally conserved current; as a consequence, their coupling to the electromagnetic field leads to extended Maxwell equations, featuring non-local, formally simple additional source terms. Solving these equations in general form or finding analytical approximations is a formidable task, but numerical solutions can be obtained by performing some bulky double-retarded integrals. We focus on concrete experimental situations which may allow to detect an anomalous quasi-static magnetic field generated by these (collective) wavefunctions in cuprate superconductors. We compute the spatial dependence of the field and its amplitude as a function of microscopic parameters including the fraction $\eta$ of supercurrent that is not locally conserved in Josephson junctions between grains, the thickness $a$ of the junctions and the size $\varepsilon$ of their current sinks and sources. The results show that the anomalous field is actually detectable at the macroscopic level with sensitive experiments, and can be important at the microscopic level because of virtual charge effects typical of the extended Maxwell equations.