https://vercosa.org/tags/complex-systems/Publicações recentes em Complex systems — Tiago LimaHugopt-BR© 2026 Tiago LimaFri, 10 Jun 2022 00:00:00 +0000https://vercosa.org/publications/turbulence-hierarchy-and-multifractality-in-the-integer-quantum-hall-transition/Fri, 10 Jun 2022 00:00:00 +0000Tiago Limahttps://vercosa.org/publications/turbulence-hierarchy-and-multifractality-in-the-integer-quantum-hall-transition/Apresentamos uma nova perspectiva sobre o problema da caracterização de flutuações mesoscópicas nas regiões entre patamares da transição do efeito Hall quântico inteiro. Constatamos que as flutuações de condutância longitudinal e transversal, geradas pela variação do campo magnético externo em um modelo microscópico, são multifratais e conduzem a distribuições de incrementos de condutância (magnetocondutância) com caudas pesadas (intermitência) e assinaturas de uma estrutura hierárquica (cascata) no processo estocástico correspondente, análogas à teoria de Kolmogorov sobre a turbulência em fluidos.<h2 id="abstract">Abstract</h2> <p>We offer a new perspective on the problem of characterizing mesoscopic fluctuations in the interplateau regions 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 (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.</p>