The Canonical Flux Quantization and IQHE(revised)

TL;DR

This paper demonstrates that canonical flux quantization leads to quantized Hall measures and explains the vanishing longitudinal resistivity in the quantum Hall effect, connecting phase space polarization with topological methods.

Contribution

It introduces a flux quantization framework based on phase space uncertainty that aligns with topological explanations of the quantum Hall effect.

Findings

Flux quantization results in quantized Hall measures.

Polarization of phase space causes zero longitudinal resistivity.

The approach is equivalent to topological methods in QHE.

Abstract

It is shown that the canonical flux quantization, which is described by the uncertainty relation on the phase space of the flux system, can result in the quantization of Hall-measures. Further it is shown that the polarization of this phase space, which is necessary for its quantization, results in the vanishing of longitudinal resistivity and conductivity. The equivalence between this approach and the topological approach to QHE is also discussed.