Quantum Statistical Singularities in Excitonic Transistors: A Mathematical Framework utilizing Ramanujan Mock Theta Functions

Quantum Statistical Singularities in Excitonic Transistors: A Mathematical Framework utilizing Ramanujan Mock Theta Functions | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Article Quantum Statistical Singularities in Excitonic Transistors: A Mathematical Framework utilizing Ramanujan Mock Theta Functions S. Eshwar Rao This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8596802/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract The semiconductor industry faces a fundamental thermodynamic barrier at the 2nm node: the ''Boltzmann Tyranny'' limits the subthreshold swing (SS) of conventional Fermionic transistors to 60 mV/dec at room temperature. This paper explores a conceptual device architecture, the Saha-Bose-Ramanujan (SBR) Framework, which proposes utilizing the collective statistics of excitons in Tungsten Diselenide (WSe$_2$) to theoretically surpass this limit. We present a phenomenological model where Saha Ionization kinetics and Bose-Einstein statistics could enable steep-slope switching near the excitonic resonance, bounded by quasiparticle lifetime broadening. Additionally, we investigate the use of Ramanujan’s Mock Theta functions as a mathematical ansatz for engineering spectral filters with super-exponential decay characteristics. Behavioral modeling suggests that such a mechanism, if physically realized, could offer parametric improvements in leakage and switching speed compared to standard drift-diffusion limits. Physical sciences/Materials science Physical sciences/Physics Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Posted Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-8596802","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":579015112,"identity":"8e736561-17b5-4478-9022-8880f2aa9bb3","order_by":0,"name":"S. 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