{"id":11869,"date":"2025-04-09T04:11:54","date_gmt":"2025-04-09T03:11:54","guid":{"rendered":"https:\/\/icertpublication.com\/?page_id=11869"},"modified":"2026-04-03T09:30:55","modified_gmt":"2026-04-03T04:00:55","slug":"study-of-anderson-localization-in-disordered-system-with-bond-breaking-disorder","status":"publish","type":"page","link":"https:\/\/icert.org.in\/index.php\/shodh-sari-2\/study-of-anderson-localization-in-disordered-system-with-bond-breaking-disorder\/","title":{"rendered":"Study of Anderson localization in disordered system with bond breaking disorder"},"content":{"rendered":"\t\t
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Shodh Sari-An International Multidisciplinary Journal<\/h1>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t
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Vol-04, Issue-02 (Apr-Jun 2025)<\/h2>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t
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An International scholarly\/ academic journal, peer-reviewed\/ refereed journal, ISSN : 2959-1376<\/h5>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t
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Study of Anderson localization in disordered system with bond breaking disorder<\/h4>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t
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Malik, Mohammed Zahid\u00a0<\/span><\/p>

North Carolina State University, US<\/span><\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t

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DOI: <\/span>https:\/\/doi.org\/10.59231\/SARI7818<\/span><\/a><\/p>

Subject: Physics \/ Condensed Matter \/ Quantum Mechanics<\/span><\/p>

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Received: Dec 23, 2024<\/span><\/p>

Accepted: Feb 05, 2025<\/span><\/p>

Published: April 01, 2025<\/span><\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t

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Thematic Classification: Anderson Localization, Disordered Systems, Bond Breaking Disorder, Quantum Transport, Physics of Materials, Statistical Mechanics.<\/span><\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t

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Abstract<\/h6>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t
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The dynamics and transport of a particle in condensed-matter systems can be described using a tight-binding Hamiltonian. In this work, we present a simple approach to investigate Anderson localization in a three-dimensional system with an off-diagonal disorder. We construct the tight-binding Hamiltonian for the system in which a single random energy is assigned to each lattice site, and the hopping integrals are restricted to nearest-neighbour sites only.\u00a0 We introduce bond-breaking disorder, where some hopping terms between sites are randomly weakened. We compute disorder-impacted density of states (DOS), the inverse participation ratio (IPR), and level statistics to identify the Anderson transition. Emergence of mobility edge has been seen while analysing inverse participation ratio with disorder.\u00a0 We address our problem in the thermodynamic limit by applying appropriate periodic boundary conditions and numerically demonstrate the existence of an Anderson localization transition.<\/span><\/p>

Keywords:<\/span> Disordered, localization, numerically, inverse participation ratio, dynamic<\/span><\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t

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Impact Statement\n<\/h6>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t
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\u00a0Our research investigates Anderson localization in disordered systems, focusing on the effects of bond-breaking disorder. Anderson localization, where the electronic wavefunctions localize due to disorder, plays a key role in understanding electronic transport properties in various materials. In this study, we explore the specific case of bond-breaking disorder, where random changes in bond strengths can disrupt the structure of the system, leading to alterations in the electronic states and transport behavior.<\/span><\/p>

We have demonstrated the Anderson transition \u2014 the shift from extended to localized electronic states \u2014 using two powerful techniques: the Inverse Participation Ratio (IPR) and level statistics. By analyzing the IPR, we identified the critical disorder strength that marks the localization transition. Furthermore, level statistics provided additional confirmation by revealing how the distribution of energy levels changes as the disorder increases. This method is sensitive to the subtle effects of bond-breaking disorder, offering deeper insights into the role of local perturbations in driving localization.<\/span><\/p>

Our findings contribute to a more nuanced understanding of Anderson localization in disordered systems, particularly in the context of bond-breaking disorder. This work not only advances theoretical models of electronic transport in disordered systems but also has significant implications for the design of materials in nanoelectronics, quantum computing, and material science, where control over disorder plays a critical role in determining device properties.\u00a0<\/span><\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t

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About The Author\n<\/h6>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t
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Dr. Mohammed Zahid Malik is a theoretical physicist specializing in Condensed Matter Physics. He is currently working as a Postdoctoral Fellow at the Department of Chemistry, North Carolina State University. His recent research work focuses on disordered systems in condensed matter theory. He has authored a paper titled “Study of Anderson Localization in Disordered System with Bond Breaking Disorder,” which explores the phenomenon of electron localization due to the presence of disorder and how bond-breaking impacts this behavior in various systems. His research contributes to the deeper understanding of electronic transport in complex and disordered materials.<\/span><\/span><\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t

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Cite this Article\n<\/h6>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t
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APA 7th Style<\/span>\u00a0<\/span><\/p>

Malik, M. Z. (2025). Study of Anderson localization in disordered system with bond breaking disorder. <\/span>Shodh Sari-An International Multidisciplinary Journal<\/span>, <\/span>4<\/span>(02), 193\u2013200. <\/span>https:\/\/doi.org\/10.59231\/SARI7818<\/span><\/a><\/p>

Chicago 17th Style<\/span>\u00a0<\/span><\/p>

Malik, Mohammed Zahid. “Study of Anderson Localization in Disordered System with Bond Breaking Disorder.” <\/span>Shodh Sari-An International Multidisciplinary Journal<\/span> 4, no. 2 (2025): 193\u2013200. <\/span>https:\/\/doi.org\/10.59231\/SARI7818<\/span><\/a>.<\/span><\/p>

MLA 9th Style<\/span>\u00a0<\/span><\/p>

Malik, Mohammed Zahid. “Study of Anderson Localization in Disordered System with Bond Breaking Disorder.” <\/span>Shodh Sari-An International Multidisciplinary Journal<\/span>, vol. 4, no. 2, 2025, pp. 193-200, <\/span>https:\/\/doi.org\/10.59231\/SARI7818<\/span><\/a>.<\/span><\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t

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Statements and Declarations\n\n<\/h6>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t
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Peer-Review Method:<\/span> This article underwent a double-blind peer-review process by two independent external experts in Quantum Physics and Condensed Matter to ensure the mathematical rigor of the localization models and the validity of the disorder analysis.<\/span><\/p>

Competing Interests:<\/span> The author Mohammed Zahid Malik declares that there are no financial, personal, or professional conflicts of interest that could have inappropriately influenced the research findings or the theoretical derivations presented in this study.<\/span><\/p>

Funding:<\/span> This research was conducted during the author’s tenure at North Carolina State University. No specific external grants or commercial funding were received for this work beyond standard institutional support.<\/span><\/p>

Data Availability:<\/span> The study is based on theoretical physics models and computational simulations. The mathematical derivations and simulation parameters used to analyze wave function localization are detailed within the paper. Additional raw data from the numerical simulations are available from the author upon reasonable request.<\/span><\/p>

Licence:<\/span> Study of Anderson localization in disordered system with bond breaking disorder<\/span> \u00a9 2025 by Mohammed Zahid Malik is licensed under <\/span>CC BY-NC-ND 4.0<\/span>. This work is published by the International Council for Education Research and Training (ICERT).<\/span><\/p>

Ethics Approval:<\/span> As this study involves theoretical physics and computational modeling without any human or animal subjects, it was deemed exempt from formal ethical review by the Institutional Research Board (IRB).<\/span><\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t

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References<\/h6>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t
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  2. Anderson, P. W. (1958). Absence of diffusion in certain random lattices. <\/span>Phys. Rev.<\/span> Reviews of Modern Physics<\/span>\u00a0<\/span>50<\/span>, (1978), <\/span>109<\/span>, 2.\u00a0N. F. Mott. Electrons in glass.<\/span><\/p><\/li>

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  4. Chalker, J. T., Pickles, T. S., & Shukla, P. (2010). Anderson localization in tight-binding models with flat bands. <\/span>Physical Review. Part B<\/span>, <\/span>82<\/span>(10). <\/span>https:\/\/doi.org\/10.1103\/PhysRevB.82.104209<\/span><\/a><\/p><\/li>

  5. Guan, C., & Guan, X. (2019). <\/span>A brief introduction to Anderson Localization<\/span>. Department of Phy, Massachusetts Institute of Technology.<\/span><\/p><\/li>

  6. Gupta, T. (2025c). Redefining Employment Relations: Understanding Recent Advances and Innovative ideas Guiding the New Era of human resource development. <\/span>Shodh Sari-An International Multidisciplinary Journal<\/span>, <\/span>04<\/span>(01), 95\u2013110. https:\/\/doi.org\/10.59231\/sari7781<\/span><\/p><\/li>

  7. E. N. Economu. <\/span>Economou Green\u2019s Functions in Quantum Physics<\/span>. (1990).<\/span><\/p><\/li>

  8. Markos, P. (2006). Numerical analysis of the Anderson localization. <\/span>Acta Physica Slovaca<\/span>, 56.<\/span><\/p><\/li>

  9. Rodr\u00edguez, A. MA MD J. R. L. G. S. V. A. M. F. D. A. J. P. L. (2001). Absence of weak localization in two-dimensional disordered Frenkel lattices. <\/span>Journal of Luminescence<\/span>, <\/span>94<\/span>.<\/span><\/p><\/li><\/ol>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t

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    Shodh Sari-An International Multidisciplinary Journal Vol-04, Issue-02 (Apr-Jun 2025) An International scholarly\/ academic journal, peer-reviewed\/ refereed journal, ISSN : 2959-1376 Study of Anderson localization in disordered system with bond breaking disorder Malik, Mohammed Zahid\u00a0 North Carolina State University, US DOI: https:\/\/doi.org\/10.59231\/SARI7818 Subject: Physics \/ Condensed Matter \/ Quantum Mechanics Page No: 193-200 Received: Dec 23, […]<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":66,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"_acf_changed":false,"postBodyCss":"","postBodyMargin":[],"postBodyPadding":[],"postBodyBackground":{"backgroundType":"classic","gradient":""},"site-sidebar-layout":"no-sidebar","site-content-layout":"page-builder","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"disabled","ast-breadcrumbs-content":"","ast-featured-img":"disabled","footer-sml-layout":"","theme-transparent-header-meta":"default","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"var(--ast-global-color-4)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"class_list":["post-11869","page","type-page","status-publish","hentry"],"acf":[],"_links":{"self":[{"href":"https:\/\/icert.org.in\/index.php\/wp-json\/wp\/v2\/pages\/11869","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/icert.org.in\/index.php\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/icert.org.in\/index.php\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/icert.org.in\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/icert.org.in\/index.php\/wp-json\/wp\/v2\/comments?post=11869"}],"version-history":[{"count":12,"href":"https:\/\/icert.org.in\/index.php\/wp-json\/wp\/v2\/pages\/11869\/revisions"}],"predecessor-version":[{"id":31787,"href":"https:\/\/icert.org.in\/index.php\/wp-json\/wp\/v2\/pages\/11869\/revisions\/31787"}],"up":[{"embeddable":true,"href":"https:\/\/icert.org.in\/index.php\/wp-json\/wp\/v2\/pages\/66"}],"wp:attachment":[{"href":"https:\/\/icert.org.in\/index.php\/wp-json\/wp\/v2\/media?parent=11869"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}