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arXiv · 2510.01584

Directionality and quantum backfire in continuous-time quantum walks from delocalized states: Exact results

Jefferson J. Ximenes·Marcelo A. Pires·José M. Villas-Bôas
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Abstract

We derive analytical results for continuous-time quantum walks from a new class of initial states with tunable delocalization. The dynamics are governed by a Hamiltonian with complex hopping amplitudes. We provide closed-form equations for key observables, revealing three notable findings: (1) the emergence of directed quantum transport from completely unbiased initial conditions; (2) a quantum backfire effect, where greater initial delocalization enhances short-time spreading but counterintuitively induces a comparatively smaller long-time spreading after a crossing time $t_{\mathrm{cross}}$; and (3) an exact characterization of survival probability, showing that the transition to an enhanced $t^{-3}$ decay is a fine-tuned effect. Our work establishes a comprehensive framework for controlling quantum transport through the interplay between intermediate initial delocalization and Hamiltonian phase.

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Jefferson J. Ximenes, Marcelo A. Pires, José M. Villas-Bôas. 2025-10-02. Directionality and quantum backfire in continuous-time quantum walks from delocalized states: Exact results. https://doi.org/10.1103/h26t-g6c7

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