Dynamics and steady states of tight-binding chains in presence of isolated defects

TL;DR

This paper investigates how a single defect in a finite periodic tight-binding chain can significantly alter wave-function spreading, leading to nonlinear effects and a defect-driven mechanism of quantum localization.

Contribution

It introduces an exact formalism for analyzing defect effects on quantum transport, revealing nonlinear phenomena and long-time localization in minimal defect scenarios.

Findings

Single defect causes non-monotonic transport suppression

Enhanced localization at distant sites due to a defect

Strong initial position sensitivity at long times

Abstract

Reduced transport and localization in isolated quantum systems are typically attributed to spatially-extended disorder, but may also emerge from the influence of a few controllable defects. We show here how a single defect profoundly reshapes wave-function spreading on a finite and periodic tight-binding lattice. Adapting the defect technique from classical random-walk studies, we obtain exact time-resolved site-occupation probabilities and several observables of interest. Even a single defect induces remarkable nonlinear effects, including non-monotonic suppression of transport, enhanced localization at distant sites, and strong sensitivity to the initial particle position at long times. These results demonstrate that minimal perturbations can generate nontrivial long-time transport signatures, giving rise to a microscopic defect-driven mechanism of quantum localization. Although the main results presented pertain to a single isolated defect, we show that the developed formalism may naturally extend to multiple as well as to a wider class of defects.