TL;DR
This paper investigates the continuous variation of the Aharonov--Bohm effect in a quantum system, showing that scattering occurs regardless of magnetic flux quantization, with potential applications in low-dimensional magnetism.
Contribution
It demonstrates that the scattering cross section in the Aharonov--Bohm effect is a continuous function of magnetic flux, extending the understanding of quantum scattering phenomena.
Findings
Scattering occurs for all magnetic flux values, not just quantized ones.
The scattering cross section varies continuously with magnetic flux.
Potential applications in soliton-magnon interactions in low-dimensional systems.
Abstract
The Aharonov--Bohm effect in a model system described by the generalized Schr\"{o}dinger equation is considered. The scattering cross section is calculated in the standard formulation: an electron beam impinges on a long impenetrable solenoid encompassing a magnetic field. It is shown that the incident wave is scattered regardless of whether the magnetic flux through the solenoid is an integer of flux quanta whereby the scattering cross section becomes a continuously nonzero function of the total magnetic flux. The problem may find its application in investigations of the soliton-magnon interaction in the low-dimensional magnetism.
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