Moving Detector Quantum Walk with Random Relocation
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Quantum Physics arXiv:2604.03593 (quant-ph) [Submitted on 4 Apr 2026] Title:Moving Detector Quantum Walk with Random Relocation Authors:Md Aquib Molla, Sanchari Goswami View a PDF of the paper titled Moving Detector Quantum Walk with Random Relocation, by Md Aquib Molla and 1 other authors View PDF HTML (experimental) Abstract:We study a discrete-time quantum walk in presence of a detector at $x_D$ initially. The detector here is repeatedly removed after a span of $t_R$, the removal time, and reinserted at random locations. Two relocation rules are considered here: In Model~1, the detector is reinserted at any site beyond $x_D$, while in Model~2, reinsertion is done within a restricted window around the position of the detector at that time. Both variants behave like Semi Infinite Walk (SIW) for large $t_R$, where the detector behaves effectively as a fixed boundary. However, in the rapid-relocation regime, i.e., when $t_R$ is small, the behaviours are different. Model~1 permits greater spreading due to unrestricted reinsertion, which is different from Model~2. The time evolution of occupation probability ratio of our walker to that of an infinite walker at $x_D$, i.e., $f(x_D,t)/f_\infty(x_D,t)$, initially show the feature of a SIW upto $t=t_R$, then show some oscillatory behaviour and finally reach a saturation value for both the models. The ratio enhancing under certain conditions of $x_D$ and $t_R$, is a purely quantum mechanical effect. The saturation ratio shows a crossover behavior below and above a removal time $t_R^*$. At sites $x \neq x_D$ the occupation probablity ratios at a certain time reveals that for small $t_R$, the behaviours of the two models are drastically different from each other, as well as from Semi Infinite Walk (SIW), Quenched Quantum Walk (QQW) and Moving Detector Quantum Walk (MDQW). The correlation ratios of the two models with that of Infinite Walk (IW) show interesting time dependence for sites to the left or right of the initial detector position $x_D$. Comments: Subjects: Quantum Physics (quant-ph); Statistical Mechanics (cond-mat.stat-mech); Computational Physics (physics.comp-ph); Instrumentation and Detectors (physics.ins-det) Cite as: arXiv:2604.03593 [quant-ph] (or arXiv:2604.03593v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2604.03593 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Sanchari Goswami [view email] [v1] Sat, 4 Apr 2026 05:12:34 UTC (170 KB) Full-text links: Access Paper: View a PDF of the paper titled Moving Detector Quantum Walk with Random Relocation, by Md Aquib Molla and 1 other authorsView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-04 Change to browse by: cond-mat cond-mat.stat-mech physics physics.comp-ph physics.ins-det References & Citations INSPIRE HEP NASA ADSGoogle Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... Data provided by: Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer (What is the Explorer?) Connected Papers Toggle Connected Papers (What is Connected Papers?) Litmaps Toggle Litmaps (What is Litmaps?) scite.ai Toggle scite Smart Citations (What are Smart Citations?) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv (What is alphaXiv?) Links to Code Toggle CatalyzeX Code Finder for Papers (What is CatalyzeX?) DagsHub Toggle DagsHub (What is DagsHub?) GotitPub Toggle Gotit.pub (What is GotitPub?) Huggingface Toggle Hugging Face (What is Huggingface?) ScienceCast Toggle ScienceCast (What is ScienceCast?) Demos Demos Replicate Toggle Replicate (What is Replicate?) Spaces Toggle Hugging Face Spaces (What is Spaces?) Spaces Toggle TXYZ.AI (What is TXYZ.AI?) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower (What are Influence Flowers?) Core recommender toggle CORE Recommender (What is CORE?) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs. Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)