Eigenspectrum and Localization for Diffusion with Traps

TL;DR

This paper studies how traps affect diffusion by analyzing the eigenspectrum and localization properties, revealing Lifshitz tail behavior and significant differences in eigenstate localization compared to trap-free diffusion.

Contribution

It provides new insights into the eigenspectrum and localization of eigenstates in diffusion with traps at critical disorder levels in two and three dimensions.

Findings

Density of states exhibits Lifshitz tail at low frequencies

Eigenstates show distinct localization properties from trap-free diffusion

Survival probability behavior aligns with Lifshitz tail analysis

Abstract

We investigate the {\em survival-return} probability distribution and the eigenspectrum for the transition probability matrix, for diffusion in the presence of perfectly absorbing traps distributed with critical disorder in two and three dimensions. The density of states is found to have a Lifshitz tail in the low frequency limit, consistent with a recent investigation of the long time behavior of the {\em survival} probability. The localization properties of the eigenstates are found to be very different from diffusion with no traps.