STATISTICS OF WAVE KINEMATICS IN RANDOM DIRECTIONAL WAVE FIELDS

Plane-wave decomposition of spatially random fields.

We investigate the uniqueness of the plane-wave decomposition of temporally deterministic, spatially random fields. Specifically, we consider the decomposition of spatially ergodic and, thus, statistically homogeneous fields. We show that when the spatial power spectrum is injective, the plane waves are the only possible coherent modes. Furthermore, the randomness of such fields originates in t...

Kinetics of scalar wave fields in random media

This paper concerns the derivation of kinetic models for high frequency scalar wave fields propagating in random media. The kinetic equations model the propagation in the phase space of the energy density of a wave field or the correlation function of two wave fields propagating in two possibly different media. Dispersive effects due to e.g. spatial and temporal discretizations, which are model...

Intermediate wave function statistics.

We calculate statistical properties of the eigenfunctions of two quantum systems that exhibit intermediate spectral statistics: star graphs and Seba billiards. First, we show that these eigenfunctions are not quantum ergodic, and calculate the corresponding limit distribution. Second, we find that they can be strongly scarred, in the case of star graphs by short (unstable) periodic orbits and, ...

Markov Random Fields in Statistics

Nonstationary random acoustic and electromagnetic fields as wave diffusion processes*

We investigate the effects of relatively rapid variations of the boundaries of an overmoded cavity on the stochastic properties of its interior acoustic or electromagnetic field. For quasi-static variations, this field can be represented as an ideal incoherent and statistically homogeneous isotropic random scalar or vector field, respectively. A physical model is constructed showing that the fi...