The nodal lines of random wave functions are investigated. We demonstrate numerically that they are well approximated by the so-called SLE6 curves which describe the continuum limit of the percolation cluster boundaries. This result gives an additional support to the recent conjecture that the nodal domains of random (and chaotic) wave functions in the semi classical limit are adequately descri...

This article analyzes the implications of protective measurement for the meaning of the wave function. According to protective measurement, a charged quantum system has mass and charge density proportional to the modulus square of its wave function. It is shown that the mass and charge density is not real but effective, formed by the ergodic motion of a localized particle with the total mass an...

We consider the homogenization of the wave equation with high frequency initial conditions propagating in a medium with highly oscillatory random coefficients. By appropriate mixing assumptions on the random medium, we obtain an error estimate between the exact wave solution and the homogenized wave solution in the energy norm. This allows us to consider the limiting behavior of the energy dens...

In this paper we analyze wave propagation in three-dimensional random media. We consider a source with limited spatial and temporal support that generates spherically diverging waves. The waves propagate in a random medium whose fluctuations have small amplitude and correlation radius larger than the typical wavelength but smaller than the propagation distance. In a regime of separation of scal...

In this paper we carry out an asymptotic analysis of the elastic wave equations in random media in the parabolic white-noise regime. In this regime, the propagation distance is much larger than the initial beam width, which is itself much larger than the typical wavelength; moreover, the correlation length of the random medium is of the same order as the initial beam width, and the amplitude of...

This paper concerns the asymptotic structure of the scintillation function in the simplified setting of wave propagation modeled by an Itô-Schrödinger equation. We show that the size of the scintillation function crucially depends on the smoothness of the initial conditions for the wave equation and on the size of the “array of detectors” where the wave fields are measured. In many practical se...