Aharonov-Bohm effect and superoscillations

TL;DR

This paper explores the Aharonov-Bohm effect and superoscillations using path-integral methods, demonstrating the supershift properties of solutions to the Schrödinger equation with this potential.

Contribution

It introduces a novel analysis of superoscillations' evolution in the Aharonov-Bohm context, employing infinite order differential operators on entire functions.

Findings

Demonstrates supershift properties of superoscillations under the Aharonov-Bohm potential

Provides a new proof based on infinite order differential operators

Connects superoscillations with quantum scattering in multiply-connected spaces

Abstract

The path-integral technique in quantum mechanics provides an intuitive framework for comprehending particle propagation and scattering. Calculating the propagator for the Aharonov-Bohm potential fits into the range of potentials in multiply-connected spaces, with the propagator represented through a series expansion. In this paper, we analyze the Schr\"odinger evolution of superoscillations, showing the supershift properties of the solution to the Schr\"odinger equation for this potential. Our proof is based on the continuity of particular infinite order differential operators acting on spaces of entire functions.