On the Applicability of the Ergodicity Hypothesis to Mesoscopic Fluctuations

TL;DR

This paper investigates whether observed non-Gaussian conductance fluctuations in mesoscopic systems are genuine or artifacts caused by correlations in magnetic field measurements, highlighting the importance of sample-dependent randomness.

Contribution

The study demonstrates that higher order cumulants of conductance fluctuations can appear non-zero due to correlations, challenging the assumption of ergodicity in mesoscopic fluctuations.

Findings

Higher cumulants have sample-dependent random parts proportional to b1 a6N 2^{n/2}\u221a(a_{n}B_{c}/B_{0})

Non-zero higher cumulants may be spurious, caused by correlations at different magnetic fields

Apparent deviations from Gaussian behavior can result from measurement correlations rather than intrinsic properties

Abstract

We evaluate a typical value of higher order cumulants (irreducible moments) of conductance fluctuations that could be extracted from magneto-conductance measurements in a single sample when an external magnetic field is swept over an interval $B_0$. We find that the n-th cumulant has a sample-dependent random part $\pm \gN 2^{n/2}\sqrt{a_{n}B_{c}/B_{0}}$, where $\gN 2$ is the variance of conductance fluctuations, $B_{c}$ is a correlation field, and $a_{n}\sim n!$. This means that an apparent deviation of the conductance distribution from a Gaussian shape, manifested by non-vanishing higher cumulants, can be a spurious result of correlations of conductances at different values of the magnetic field.