Defect-Driven Nonlinear and Nonlocal Perturbations in Quantum Chains

Abstract: Transport and localization in isolated quantum systems are typically attributed to spatially-extended disorder, leaving the influence of a few controllable defects largely unexplored despite their relevance to engineered quantum platforms. We introduce an analytic framework showing how a single defect profoundly reshapes wave-function spreading on a finite isolated 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 one defect induces striking nonlinear and nonlocal 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 unexpected long-time transport signatures, establishing a microscopic defect-driven mechanism of quantum localization.