Coherence and realism in the Aharonov-Bohm effect

TL;DR

This paper investigates the Aharonov-Bohm effect using an entropic measure called realism, revealing a sudden change in realism related to gauge invariance and analyzing effects of quantized magnetic sources.

Contribution

It introduces a novel entropic measure of realism to analyze the Aharonov-Bohm effect and identifies a sudden change in realism linked to the wave packets crossing the solenoid.

Findings

Realism exhibits a sudden change when wave packets cross the solenoid.

Gauge-invariant observables are identified that relate to the system's realism.

Differences are noted between classical and quantized magnetic field sources.

Abstract

The Aharonov-Bohm effect is a fundamental topological phenomenon with a wide range of applications. It consists of a charge encircling a region with a magnetic flux in a superposition of wave packets having their relative phase affected by the flux. In this work, we analyze this effect using an entropic measure known as realism, originally introduced as a quantifier of a system's degree of reality and mathematically related to notions of global and local quantum coherence. More precisely, we look for observables that lead to gauge-invariant realism associated with the charge before it completes its loop. We find that the realism of these operators has a sudden change when the line connecting the center of both wave packets crosses the solenoid. Moreover, we consider the case of a quantized magnetic-field source, pointing out similarities and differences between the two cases. Finally, we discuss some consequences of these results.