Dynamics of Localized Waves

TL;DR

This study investigates microwave transmission in quasi-1D samples, revealing how transmission decay transitions from diffusive to localized behavior over time, aligning with theoretical models and simulations.

Contribution

It provides experimental validation of the self-consistent theory of localization and introduces a dynamic single parameter scaling model for long-time decay.

Findings

Transmission remains diffusive up to four times the diffusion time.

Decay rate deviates from self-consistent theory at longer times.

Long-lived localized modes dominate decay beyond the Heisenberg time.

Abstract

We have measured pulsed microwave transmission through quasi-1D samples with lengths up to three localization lengths. For times approaching four times the diffusion time \tau_D, transmission is diffusive in accord with the self-consistent theory of localization for the renormalized diffusion coefficient in space and frequency, D(z,\Omega). For longer times, the transmission decay rate first agrees with and later falls increasingly below the self-consistent theory. Beyond the Heisenberg time, the decay rate approaches the predictions of a dynamic single parameter scaling model which reflects the decay of long-lived localized modes and converges to the results of 1D simulations.