Brownian windings, Stochastic Green's formula and inhomogeneous magnetic impurities
Isao Sauzedde
TL;DR
This paper develops a Green formula for planar Brownian motion to analyze the Aharonov--Bohm effect caused by randomly distributed magnetic impurities in an inhomogeneous magnetic field.
Contribution
It introduces a general Green formula for planar Brownian motion and applies it to study quantum effects of magnetic impurities.
Findings
Derived a new Green formula for planar Brownian motion
Analyzed the impact of magnetic impurities on the Aharonov--Bohm effect
Provided insights into electron behavior in inhomogeneous magnetic fields
Abstract
We give a general Green formula for the planar Brownian motion, which we apply to study the Aharonov--Bohm effect induced by Poisson distributed magnetic impurities on a Brownian electron in the presence of an inhomogeneous magnetic field.
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Taxonomy
TopicsSpectral Theory in Mathematical Physics · Quantum and electron transport phenomena · Theoretical and Computational Physics