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

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

2000-05-02

arxiv.org/abs/cond-mat/0005042v2

Phys.Rev.Lett. 85, 3388 (2000)

Physics

Condensed Matter

Disordered Systems and Neural Networks

4 pages, 1 figure, reorganized version

Scientific paper

10.1103/PhysRevLett.85.3388

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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