Quantum walker trapped by self-similarity of the Sierpi\'nski carpet

Abstract:We study the dynamics of a single quantum particle on a finite-size square lattice with a fractal structure resembling the Sierpiński carpet, and compare it to the dynamics on a uniform lattice of the same size. For a particle initially localized at a corner of the lattice, we monitor the probability of finding it near the initial and opposite corners using zone-integrated probabilities, allowing a consistent comparison across fractal orders. While on the uniform lattice the particle reaches the opposite corner ballistically, in a time proportional to the lattice size, on the Sierpiński lattice it becomes increasingly confined to the vicinity of its initial position. We show that this trapping builds up self-similarly across the whole hierarchy of corner zones of the lattice.

arXiv:2608.04844 [quant-ph]

(or arXiv:2608.04844v1 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2608.04844 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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