Turbulence Hierarchy and Multifractality in the Integer Quantum Hall Transition

TL;DR

This paper reveals that mesoscopic conductance fluctuations in the integer quantum Hall transition exhibit multifractality, hierarchy, and intermittency, similar to fluid turbulence, using stochastic analysis and H-theory.

Contribution

It introduces a novel multifractal stochastic framework for understanding conductance fluctuations in the quantum Hall transition, linking turbulence concepts to quantum mesoscopic phenomena.

Findings

Conductance fluctuations are multifractal and heavy-tailed.

Evidence of hierarchical cascade structures in conductance data.

Validation of the turbulence analogy through H-theory analysis.

Abstract

We offer a new perspective to the problem of characterizing mesoscopic fluctuations in the inter-plateau region of the integer quantum Hall transition. We found that longitudinal and transverse conductance fluctuations, generated by varying the external magnetic field within a microscopic model, are multifractal and lead to distributions of conductance increments (magnetoconductance) with heavy tails (intermittency) and signatures of a hierarchical structure (a cascade) in the corresponding stochastic process, akin to Kolmogorov's theory of fluid turbulence. We confirm this picture by interpreting the stochastic process of the conductance increments in the framework of H-theory, which is a continuous-time stochastic approach that incorporates the basic features of Kolmogorov's theory. The multifractal analysis of the conductance "time series," combined with the H-theory formalism provides, strong support for the overall characterization of mesoscopic fluctuations in the quantum Hall transition as a multifractal stochastic phenomenon with multiscale hierarchy, intermittency, and cascade effects.