Applicability of the ergodicity hypothesis to mesoscopic fluctuations

2003/06/24 by Oleksandr Tsyplyatyev, O. Tsyplyatyev, I. L. Aleiner +4
Mathematics · Physics and Astronomy · #Condensed matter physics #Conductance #Cumulant #Ergodicity #Gaussian #Mathematics #Mesoscopic physics #Physics #Quantum and electron transport phenomena #Quantum many-body systems #Quantum mechanics #Spurious relationship #Statistical physics #Statistics #Theoretical and Computational Physics #cond-mat.dis-nn #cond-mat.mes-hall

paper · pdf · doi:10.1103/physrevb.68.121301

published as Phys. Rev. B (RC), 68, 121301 (2003) · 4 pages, no figures, submitted to Phys. Rev. B

arxiv created 2003/06/24 · openalex publication_date 2003/09/11 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

We evaluate a typical value of higher-order cumulants (irreducible moments) of conductance fluctuations that could be extracted from magnetoconductance measurements in a single sample when an external magnetic field is swept over an interval B₀. We find that the nth cumulant has a sample-dependent random part \ifmmode±\else\textpm\fi〈〈g²〉〉^n/2√a_nB_c/B₀, where 〈〈g²〉〉 is the variance of conductance fluctuations, B_c is a correlation field, and a_n\ensuremath∼n! This means that an apparent deviation of the conductance distribution from a Gaussian shape, manifested by nonvanishing higher cumulants, can be a spurious result of correlations of conductances at different values of the magnetic field.

Citations

• Conductance fluctuations due to a bistable scatterer in a weakly connected conductor
• Multifractality: Generic Property of Eigenstates of 2D Disordered Metals
• Scaling Theory of Localization: Absence of Quantum Diffusion in Two Dimensions
• Anomalous Conductance Distribution in Quasi-One-Dimensional Gold Wires: Possible Violation of the One-Parameter Scaling Hypothesis
• Deviations from the Gaussian distribution of mesoscopic conductance fluctuations