Universal Statistics of Waves in a Random Time-Varying Medium
Rémi Carminati, H. Chen, Romain Pierrat, Boris Shapiro
Abstract
We study the propagation of waves in a medium in which the wave velocity fluctuates randomly in time. We prove that at long times, the statistical distribution of the wave energy is log-normal, with the average energy growing exponentially. For weak disorder, another regime preexists at shorter times, in which the energy follows a negative exponential distribution, with an average value growing linearly with time. The theory is in perfect agreement with numerical simulations, and applies to different kinds of waves. The existence of such universal statistics bridges the fields of wave propagation in time-disordered and space-disordered media.
Topics & Concepts
PhysicsEnergy (signal processing)Distribution (mathematics)Statistical physicsStatisticsRandom matrixExponential functionExponential distributionSpace (punctuation)Wave propagationQuantum mechanicsMathematical analysisMathematicsComputer scienceOperating systemEigenvalues and eigenvectorsRandom lasers and scattering mediaQuantum optics and atomic interactionsOptical and Acousto-Optic Technologies