Uncertainty Relation For Quantized Magnetic Fields and The Quantum Hall Effect

TL;DR

This paper proposes an uncertainty relation connecting the Hall potential and gate potential in the quantum Hall effect, providing a new theoretical perspective on quantized magnetic fields.

Contribution

It introduces an uncertainty relation model that describes the relationship between Hall and gate potentials in the quantum Hall effect.

Findings

The relation between Hall potential and gate potential is characterized by an uncertainty relation.

The model explains the stepped curve observed in the quantum Hall effect.

Provides a theoretical framework linking magnetic field quantization and potential fluctuations.

Abstract

We discuss a model where the relation between Hall potential $A_H$ = and gate potential $A_G$, which is manifested by the stepped QHE = curve, is described by an uncertainty relation $\Delta A_H . = \Delta A_G =3D B(\hbar/e)$.