Figure 1

Comparison of quantum mechanical and classical density calculations. (a),(b) Numerical simulations of a quantum mechanical (a) and of a classical flow (b) propagating through the same weak random potential (shaded background) starting from a plane wave initial condition. The gray scale superimposed on the potential indicates the flow intensity. The statistics of the intensities in (c) is measured at the location of the vertical lines to the right of the top panels. (c) Classical and two quantum intensity distributions (obtained from 100 realizations of the random potential) in a rescaled log-log plot in which the log-normal distribution appears as an inverse parabola. The classical flow can be approximated by a log-normal distribution, whereas the quantum mechanical statistics follows Rayleigh’s exponential law.Reuse & Permissions

Figure 2

Examples of wave flows averaged over 100 realizations of the random phases ${\phi }_j$ for $\gamma =1$ (coherent), $\gamma =1/2$ (intermediate), and $\gamma =0$ (incoherent). The propagation of a single initial wave function ${\psi }_j^0$ is superimposed (red online) in the top panel. Darker shades of gray (gray and red online) indicate higher flow intensity.Reuse & Permissions

Figure 3

Intensity distribution $P(I,\gamma ,\mu ,\sigma ,a)$ for different values of the coherence parameter $\gamma$. The lines are the analytical results from Eq. (2), the circles are the numerical data. In the upper panel, a log-linear plot illustrates the correct scaling of the tails as predicted by the analytics. In the inset, a linear plot shows that the rest of the probability distribution is in excellent agreement also. The lower panel shows the same curves, rescaled, as in Fig. 1. It illustrates the growth of the heavy tail of $P(I)$ as it changes from exponential to log-normal for decreasing $\gamma$.Reuse & Permissions