Quantum walker trapped by self-similarity of the Sierpiński carpet

• URL: http://arxiv.org/abs/2608.04844v1
• Date: Wed, 05 Aug 2026 13:37:41 GMT
• Title: Quantum walker trapped by self-similarity of the Sierpiński carpet
• Abstract summary: We study the dynamics of a single quantum particle on a finite-size square lattice with a fractal structure resembling the Sierpiski carpet.<n>We show that this trapping builds up self-similarly across the whole hierarchy of corner zones of the lattice.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

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