Fluctuations of local density of states and $C_0$ speckle correlations are equal

We establish a conceptual relation between the fluctuations of the local density of states (LDOS) and the intensity correlations in speckle patterns resulting from the multiple scattering of waves in random media. We show that among the known types of speckle correlations ($C_1$, $C_2$, $C_3$, and $C_0$) only $C_0$ contributes to LDOS fluctuations in the infinite medium. We propose to exploit the equivalence of LDOS fluctuations and the $C_0$ intensity correlation as a “selection rule” for scattering processes contributing to $C_0$.

Figure 1

(a) Two-field intensity diagrams that give the leading order to the variance of the LDOS in a random medium with Gaussian uncorrelated disorder. (b) Typical four-field diagrams that contribute to speckle correlations in a random medium. Solid and dashed lines denote retarded and advanced Green’s functions, respectively, shaded boxes are ladder propagators $\left(L\right)$ and Hikami boxes $\left(H\right)$, the dotted line with crosses denotes scattering of two wave fields on the same heterogeneity. The variance of the LDOS can be obtained by integrating over $\mathbf{x}$ and ${\mathbf{x}}^{\prime }$. Only the lower right diagram yields a nonvanishing contribution to the variance of the LDOS in the infinite medium.