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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2601.16111 |
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| _version_ | 1866918300054716416 |
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| author | Singh, Prashant Kessler, David A. Barkai, Eli |
| author_facet | Singh, Prashant Kessler, David A. Barkai, Eli |
| contents | We investigate the splitting probability of a monitored continuous-time quantum walk with two targets and show that, in stark contrast to a classical random walk, it exhibits a nonanalytic, phase-transition-like behavior controlled by the sampling time at the targets. For large systems and sampling times smaller than a critical value $τ_c = 2π/ΔE$, where $ΔE$ is the energy bandwidth, the splitting probability is universal and equal to $1/2$, independent of the initial condition and the sampling time. Above the critical sampling, a nonuniversal regime emerges in which the splitting probability deviates from $1/2$ and develops a fluctuating pattern of pronounced peaks and dips dependent on both the sampling time and the initial condition. These results follow from a nontrivial mapping of the splitting problem onto a pair of single-target detection problems enabled by the superposition principle. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_16111 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Transition in Splitting Probabilities of Quantum Walks Singh, Prashant Kessler, David A. Barkai, Eli Statistical Mechanics We investigate the splitting probability of a monitored continuous-time quantum walk with two targets and show that, in stark contrast to a classical random walk, it exhibits a nonanalytic, phase-transition-like behavior controlled by the sampling time at the targets. For large systems and sampling times smaller than a critical value $τ_c = 2π/ΔE$, where $ΔE$ is the energy bandwidth, the splitting probability is universal and equal to $1/2$, independent of the initial condition and the sampling time. Above the critical sampling, a nonuniversal regime emerges in which the splitting probability deviates from $1/2$ and develops a fluctuating pattern of pronounced peaks and dips dependent on both the sampling time and the initial condition. These results follow from a nontrivial mapping of the splitting problem onto a pair of single-target detection problems enabled by the superposition principle. |
| title | Transition in Splitting Probabilities of Quantum Walks |
| topic | Statistical Mechanics |
| url | https://arxiv.org/abs/2601.16111 |