General theory of perturbation of infinite resistor networks

[2506.18654] General theory of perturbation of infinite resistor networks Skip to main content Search Submit Donate Log in Mathematical Physics arXiv:2506.18654 (math-ph) [Submitted on 23 Jun 2025 ( v1 ), last revised 24 Nov 2025 (this version, v3)] Title: General theory of perturbation of infinite resistor networks Authors: József Cserti , Gyula Dávid View PDF HTML (experimental) Abstract: The effective resistance between any two nodes in a perturbed resistor network is determined by removing multiple bonds from an infinite resistor lattice. We have developed an efficient method for calculating the Green operator of the Laplacian for such perturbed networks, which is directly related to the two-point resistance. Unlike the recursive techniques that remove bonds one at a time, our approach handles all bond modifications simultaneously. To demonstrate the versatility of our method, several analytical and numerical examples are presented. In addition, we computed bond current distributions to gain deeper insight into the nature of resistor perturbations. We emphasize that our method has a broad range of applications, including condensed matter physics describing the quantum mechanical effects of impurities in crystal lattices, recently emerging topoelectronics, the study of vibrations in spring networks, and problems involving random walks. Comments: 16 figures, 31 pages Subjects: Mathematical Physics (math-ph) ; Statistical Mechanics (cond-mat.stat-mech) Cite as: arXiv:2506.18654 [math-ph] (or arXiv:2506.18654v3 [math-ph] for this version) https://doi.org/10.48550/arXiv.2506.18654 Focus to learn more arXiv-issued DOI via DataCite Journal reference: J. Phys. A: Math. Theor. 59 (2026) 025202 Related DOI : https://doi.org/10.1088/1751-8121/ae3407 Focus to learn more DOI(s) linking to related resources Submission history From: Jozsef Cserti [ view email ] [v1] Mon, 23 Jun 2025 13:55:24 UTC (157 KB) [v2] Wed, 16 Jul 2025 12:36:36 UTC (157 KB) [v3] Mon, 24 Nov 2025 13:37:39 UTC (276 KB) Full-text links: Access Paper: View PDF HTML (experimental) TeX Source view license Current browse context: math-ph < prev | next > new | recent | 2025-06 Change to browse by: cond-mat cond-mat.stat-mech math math.MP References & Citations SciX Google Scholar Semantic Scholar export BibTeX citation 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? ) We gratefully acknowledge support from our major funders , member institutions , and all contributors. About · Help · Contact · Subscribe · Copyright · Privacy · Accessibility · Operational Status (opens in new tab)

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