Impact of Weak Localization on Wave Dynamics: Crossover from Quasi-1D to Slab Geometry

TL;DR

This paper investigates how weak localization affects wave dynamics in diffusive samples, revealing a crossover from quasi-one-dimensional to slab geometry and how the diffusion coefficient evolves over time.

Contribution

It introduces a detailed analysis of wave propagation using the Bethe-Salpeter equation with recurrent scattering, highlighting the geometry-dependent renormalization of the mean free path.

Findings

D(t) decreases linearly after pulse peak with a slope depending on geometry.

The initial diffusion coefficient depends on the dimensionless conductance g or on kl and L.

A crossover from quasi-1D to slab geometry significantly alters wave diffusion behavior.

Abstract

We study the dynamics of wave propagation in nominally diffusive samples by solving the Bethe-Salpeter equation with recurrent scattering included in a frequency-dependent vertex function, which renormalizes the mean free path of the system. We calculate the renormalized time-dependent diffusion coefficient, D(t), following pulsed excitation of the system. For cylindrical samples with reflecting side walls and open ends, we observe a crossover in dynamics in the transformation from a quasi-1D to a slab geometry implemented by varying the ratio of the radius, R, to the length, L. Immediately after the peak of the transmitted pulse, D(t) falls linearly with a nonuniversal slope that approaches an asymptotic value for R/L>>1. The value of D(t) extrapolated to t=0, depends only upon the dimensionless conductance g for R/L<<1 and upon kl and L for R/L>>1, where k is the wave vector and l is the bare mean free path.