An Exactly Solvable Absorbing Quantum Walk
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866914574144372736 |
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| author | Riberi, Francisco |
| author_facet | Riberi, Francisco |
| contents | We introduce and solve from first principles a continuous-time quantum walk with absorption generated by a Lindblad boundary sink of arbitrary strength. Tracing out the sink maps the problem onto a non-Hermitian tight-binding Hamiltonian with a rank-one imaginary defect on the semi infinite line. We obtain closed-form expressions for the exact propagator and first-passage statistics. Weak coupling limits absorption through inefficient transfer into the sink, whereas for strong dissipation, boundary occupation is stunted by the emergence of a localized non-Hermitian mode. Despite the different physical origin of these suppression mechanisms, we show their respective asymptotic absorption probabilities exhibits an exact duality. The evolution is conveniently visualized in phase-space, where the non-Hermitian mode produces a Wigner droplet exponentially confined near the edge site. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_08056 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | An Exactly Solvable Absorbing Quantum Walk Riberi, Francisco Quantum Physics We introduce and solve from first principles a continuous-time quantum walk with absorption generated by a Lindblad boundary sink of arbitrary strength. Tracing out the sink maps the problem onto a non-Hermitian tight-binding Hamiltonian with a rank-one imaginary defect on the semi infinite line. We obtain closed-form expressions for the exact propagator and first-passage statistics. Weak coupling limits absorption through inefficient transfer into the sink, whereas for strong dissipation, boundary occupation is stunted by the emergence of a localized non-Hermitian mode. Despite the different physical origin of these suppression mechanisms, we show their respective asymptotic absorption probabilities exhibits an exact duality. The evolution is conveniently visualized in phase-space, where the non-Hermitian mode produces a Wigner droplet exponentially confined near the edge site. |
| title | An Exactly Solvable Absorbing Quantum Walk |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2605.08056 |