Signature of wave localisation in the time dependence of a reflected pulse
Titov, M. · Beenakker, C. W. J.
Original · EN
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 N² 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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