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Turbulence Hierarchy and Multifractality in the Integer Quantum Hall Transition.

Anderson L R Barbosa¹, Tiago H V de Lima¹, Iván R R González^2,3

¹Departamento de Física, Universidade Federal Rural de Pernambuco, Recife-PE 52171-900, Brazil.

Physical Review Letters

|June 24, 2022

Summary

Mesoscopic fluctuations in the quantum Hall transition exhibit multifractal behavior, characterized by intermittency and cascade effects akin to fluid turbulence. This study reveals a hierarchical structure in conductance increments, offering a new perspective on these complex phenomena.

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Area of Science:

Condensed Matter Physics
Statistical Physics

Background:

Mesoscopic fluctuations in the integer quantum Hall transition present complex characteristics.
Understanding these fluctuations is crucial for characterizing the quantum Hall effect.

Purpose of the Study:

To offer a new perspective on characterizing mesoscopic fluctuations in the integer quantum Hall transition.
To analyze the nature of longitudinal and transverse conductance fluctuations.

Main Methods:

Microscopic model to generate conductance fluctuations by varying magnetic field.
Multifractal analysis of conductance time series.
Interpretation using H theory, a continuous-time stochastic approach.

Main Results:

Longitudinal and transverse conductance fluctuations exhibit multifractal properties.
Conductance increments show heavy tails (intermittency) and hierarchical structure (cascade).
The stochastic process aligns with Kolmogorov's theory of fluid turbulence.

Conclusions:

Mesoscopic fluctuations in the quantum Hall transition are a multifractal stochastic phenomenon.
The study supports a characterization involving multiscale hierarchy, intermittency, and cascade effects.
H theory provides a framework for understanding these complex dynamics.