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

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.

arXiv comment4 pages, 1 figure, reorganized version

References in corpus (5)

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• Nearly Localized States in Weakly Disordered Conductor
• Probability of Reflection by a Random Laser
• Equivalence of Fokker-Planck approach and non-linear $\sigma$-model for disordered wires in the unitary symmetry class
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Cited by in corpus (14)

• Dynamics of Anderson localization in open 3D media
• Dynamics of weakly localized waves
• Random matrices beyond the Cartan classification
• Fokker-Planck equations and density of states in disordered quantum wires
• Statistics of Dynamics of Localized Waves
• Supersymmetric field theory of local light diffusion in semi-infinite media
• Dynamic Correlation in Wave Propagation in Random Media
• Time-dependent reflection at the localization transition
• Quantum mechanical relaxation of open quasiperiodic systems
• Transmission delay times of localized waves
• Dynamics of classical wave scattering by small obstacles
• Random matrix theory of proximity effect in disordered wires
• Andreev levels in a single-channel conductor
• Dynamic effect of phase conjugation on wave localization