Fig. 4

Symmetry-class dependence of the one-parameter scaling function β(g). a, b Time-evolution of \(\left\langle {p_1^2} \right\rangle\) in the weak-localization regime in the two symmetry classes. In the orthogonal class (a), closed-loop corrections lead to a rapid deviation from classical diffusion (dashed line). In the unitary class (b), these corrections are absent, which qualitatively translates in a much slower departure from classical diffusion. In both cases, D₀ is the same within ~20%. c Experimental dependence of the β(g) function on the dimensionless conductance \(g = N\sqrt {\left\langle {p_1^2} \right\rangle } {\mathrm{/}}(\hbar_{\mathrm{e}} t)\), measured following the 1D spreading of a wave packet in momentum space. The error bars represent the typical uncertainty coming from the experimental determination of \(\left\langle {p_1^2} \right\rangle\). The different symbols (circles, diamonds and squares) correspond to three sets of different microscopic parameters (K and N) of the system: (K, N) ∈ {(4, 3), (4.5, 4), (3.5, 5)} (orthogonal, orange) and respectively (K, N) ∈ {(2.5, 3), (4, 4), (1.6, 5)} (unitary, blue), for a value of \(\hbar_{\mathrm{e}}=1\) . All data in each class collapse onto two distinct universal β(g) functions, characteristic of each symmetry class, indicated by the shaded regions. The asymptotic behavior at large g is correctly predicted by Eq. (6) (continuous lines) inside their domain of validity