Self-Averaging of Wigner Transforms in Random Media

  title={Self-Averaging of Wigner Transforms in Random Media},
  author={Guillaume Bal and Tomasz Komorowski and Lenya Ryzhik},
  journal={Communications in Mathematical Physics},
AbstractWe establish the self-averaging properties of the Wigner transform of a mixture of states in the regime when the correlation length of the random medium is much longer than the wave length but much shorter than the propagation distance. The main ingredients in the proof are the error estimates for the semiclassical approximation of the Wigner transform by the solution of the Liouville equations, and the limit theorem for two-particle motion along the characteristics of the Liouville… 
On the Self-Averaging of Wave Energy in Random Media
  • G. Bal
  • Mathematics
    Multiscale Model. Simul.
  • 2004
It is shown that wave energy is not stable, and instead scintillation is created by the wave dynamics, when the initial energy distribution is sufficiently singular.
Self-Averaging from Lateral Diversity in the Itô-Schrödinger Equation
The Wigner transform of the wave field is used and it is shown that it becomes deterministic in the large diversity limit when integrated against test functions and also shows that the limit is deterministic when the support of the test functions tends to zero but is large compared to the correlation length.
Wave field correlations in weakly mismatched random media
This paper concerns the derivation of a Fokker-Planck equation for the correlation of two high frequency wave fields propagating in two different random media. The mismatch between the random media
Self-averaging of kinetic models for waves in random media
Kinetic equations are often appropriate to model the energy density of high frequency waves propagating in highly heterogeneous media. The limitations of the kinetic model are quantified by the
Wave Decoherence for the Random Schrödinger Equation with Long-Range Correlations
In this paper, we study the loss of coherence of a wave propagating according to the Schrödinger equation with a time-dependent random potential. The random potential is assumed to have slowly
Time Reversal in Changing Environments
This paper analyzes the refocusing properties of time-reversed acoustic waves that propagate in different media during the forward and backward propagation phases. We show how the refocused signal is
The Random Schrödinger Equation: Homogenization in Time-Dependent Potentials
It is shown that the dynamics generates a non-trivial energy in the high frequencies, which do not homogenize -- the high frequency component of the wave field remains random and the evolution of its energy is described by a kinetic equation.
Stability of time reversed waves in changing media
We analyze the refocusing properties of time reversed waves that propagate in two different media during the forward and backward stages of a time-reversal experiment. We consider two regimes of


We analyze the self-averaging properties of time-reversed solutions of the paraxial wave equation with random coefficients, which we take to be Markovian in the direction of propagation. This allows
Homogenization limits and Wigner transforms
We present a theory for carrying out homogenization limits for quadratic functions (called “energy densities”) of solutions of initial value problems (IVPs) with anti-self-adjoint (spatial)
Time Reversal for Waves in Random Media
In time reversal acoustics experiments, a signal is emitted from a localized source, recorded at an array of receivers-transducers, time reversed, and finally re-emitted into the medium. A celebrated
Time Reversal and Refocusing in Random Media
A quantitative explanation of time reversal and other more general refocusing phenomena for general classical waves in heterogeneous media is presented based on the asymptotic analysis of the Wigner transform of wave fields in the high frequency limit.
Sur les mesures de Wigner
We study the properties of the Wigner transform for arbitrary functions in L2 or for hermitian kernels like the so-called density matrices. And we introduce some limits of these transforms for
Statistical Stability in Time Reversal
The refocusing resolution in a high frequency remote-sensing regime is analyzed and it is shown that, because of multiple scattering in an inhomogeneous or random medium, it can improve beyond the diffraction limit.
Focusing of time-reversed reflections
Abstract Recently time-reversal techniques have emerged as a new, important and fascinating discipline within wave propagation. Many of the problems involved can best be understood, analysed and
Super-resolution in time-reversal acoustics.
The phenomenon of super-resolution in time-reversal acoustics is analyzed theoretically and with numerical simulations and numerical simulations confirm the theory.