Impact of weak localization in the time domain

Area of Science:

• Condensed matter physics
• Wave propagation in disordered media
• Transport phenomena

Background:

• Understanding wave transport in diffusive media is crucial for various physical phenomena.
• The Bethe-Salpeter equation is a powerful tool for describing wave scattering and localization.
• Sample geometry significantly influences transport properties.

Purpose of the Study:

• To investigate the time-dependent diffusion coefficient, D(t), in a diffusive sample under pulsed excitation.
• To explore the crossover in dynamics from quasi-1D to slab geometry.
• To analyze the dependence of D(t) on sample dimensions and intrinsic material properties.

Main Methods:

• Solving the Bethe-Salpeter equation with recurrent scattering.
• Utilizing pulsed excitation to probe dynamic responses.
• Systematically varying the sample geometry (radius R to length L ratio) of a cylinder with reflecting side walls and open ends.

Main Results:

• A renormalized time-dependent diffusion coefficient, D(t), was identified.
• A crossover in dynamics was observed as the geometry transitioned from quasi-1D to slab-like.
• Immediately after pulse peak, D(t) exhibited linear decay with a nonuniversal slope, approaching an asymptotic value for large R/L.
• Extrapolated D(t) at t=0 showed dependence on dimensionless conductance g for R/L<<1 and on kl(0) for R/L>>1.

Conclusions:

• The study reveals a geometry-dependent crossover in wave transport dynamics.
• The time-dependent diffusion coefficient is a key parameter characterizing this transition.
• The findings provide insights into wave propagation in finite-sized diffusive systems.