Signature of wave localisation in the time dependence of a reflected pulse

M. Titov; C. W. J. Beenakker

doi:10.1103/physrevlett.85.3388

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Signature of wave localisation in the time dependence of a reflected pulse

M. Titov·C. W. J. Beenakker

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Abstract

The average power spectrum of a pulse reflected by a disordered medium embedded in an N-mode waveguide decays in time with a power law t^(-p). We show that the exponent p increases from 3/2 to 2 after N^2 scattering times, due to the onset of localisation. We compare two methods to arrive at this result. The first method involves the analytic continuation to imaginary absorption rate of a static scattering problem. The second method involves the solution of a Fokker-Planck equation for the frequency dependent reflection matrix, by means of a mapping onto a problem in non-Hermitian quantum mechanics.

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M. Titov, C. W. J. Beenakker. 2000-08-04. Signature of wave localisation in the time dependence of a reflected pulse. https://doi.org/10.1103/physrevlett.85.3388

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