On the Applicability of the Ergodicity Hypothesis to Mesoscopic Fluctuations

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 $\pm \text{gN}{2}^{n\mathrm{/}2}\sqrt{a_n{B}_c\mathrm{/}{B}_0}$, where $\text{gN}2$ 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.