Cross-Time Memory Kernelsin Macroscopic Quantum TunnelingNon-Markovian Signatures in Josephson Junctions

Cross-Time Memory Kernelsin Macroscopic Quantum TunnelingNon-Markovian Signatures in Josephson Junctions | 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 Research Article Cross-Time Memory Kernelsin Macroscopic Quantum TunnelingNon-Markovian Signatures in Josephson Junctions Mahgoub A. Salih, Mohamed Y. Shirgawi This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-9103716/v1 This work is licensed under a CC BY 4.0 License Status: Under Revision Version 1 posted 10 You are reading this latest preprint version Abstract When a Josephson junction is coupled to an environment with memory time $\lambda_c^{-1}$ exceeding a dynamically engineered suppression window $[t_1,t_2]$, bath-mediated correlations link pre-window and post-window tunneling events in a way that no local-in-time escape rate can reproduce. Using the Caldeira--Leggett influence-functional framework, we derive a Volterra integro-differential survival equation containing, alongside the usual Markovian and local-memory terms, an explicit \emph{cross-time} kernel $K_{\text{cross}}(t,t')$ that couples times $tt_2$ while contributions from within the suppressed interval remain exponentially small. The resulting switching-time distribution displays two separable signatures: a clustering peak at $t_2$ with jump ratio $\varepsilon^{-1}$ ($\varepsilon \ll 1$ being the in-window rate suppression), and a post-window memory tail whose decay constant equals the bath correlation rate $\lambda_c$ and whose \emph{amplitude} is set by the pre-window history functional $M_{\text{pre}}$. The amplitude also scales as $e^{-\lambda_c \Delta t_b}$ with $\Delta t_b = t_2 - t_1$, providing a direct spectroscopic handle on the bath memory time. Standard resistively shunted junctions, with $\lambda_c^{-1} \sim 10,\text{ps}$, render the cross-time signal unobservable for nanosecond barriers; coupling the junction to a high-$Q$ microwave resonator ($Q \sim 10^5$, $\omega_r/2\pi \sim 5,\text{GHz}$) extends the effective memory time to microseconds, bringing both signatures within reach of current superconducting circuit technology. \bigskip\noindent\textbf{Keywords:} Non-Markovian dynamics; Cross-time memory kernels; Macroscopic quantum tunneling; Josephson junctions; Switching-time distribution; Caldeira--Leggett model; Volterra integro-differential equations; Bath correlation spectroscopy Non-Markovian dynamics Cross-time memory kernels Macroscopic quantum tunneling Josephson junctions Switching-time distribution Caldeira– Leggett model Volterra integro-differential equations Bath correlation spectroscopy Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Under Revision Version 1 posted Editorial decision: Revision requested 18 May, 2026 Reviews received at journal 03 May, 2026 Reviews received at journal 21 Apr, 2026 Reviewers agreed at journal 20 Apr, 2026 Reviewers agreed at journal 14 Apr, 2026 Reviewers invited by journal 24 Mar, 2026 Editor invited by journal 24 Mar, 2026 Editor assigned by journal 24 Mar, 2026 Submission checks completed at journal 23 Mar, 2026 First submitted to journal 23 Mar, 2026 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-9103716","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":612228457,"identity":"0d535fbd-657c-427f-bc2a-d64978567067","order_by":0,"name":"Mahgoub A. 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Using the Caldeira--Leggett influence-functional framework, we derive a Volterra integro-differential survival equation containing, alongside the usual Markovian and local-memory terms, an explicit \\emph{cross-time} kernel $K_{\\text{cross}}(t,t')$ that couples times $tt_2$ while contributions from within the suppressed interval remain exponentially small. The resulting switching-time distribution displays two separable signatures: a clustering peak at $t_2$ with jump ratio $\\varepsilon^{-1}$ ($\\varepsilon \\ll 1$ being the in-window rate suppression), and a post-window memory tail whose decay constant equals the bath correlation rate $\\lambda_c$ and whose \\emph{amplitude} is set by the pre-window history functional $M_{\\text{pre}}$. The amplitude also scales as $e^{-\\lambda_c \\Delta t_b}$ with $\\Delta t_b = t_2 - t_1$, providing a direct spectroscopic handle on the bath memory time. Standard resistively shunted junctions, with $\\lambda_c^{-1} \\sim 10\\,\\text{ps}$, render the cross-time signal unobservable for nanosecond barriers; coupling the junction to a high-$Q$ microwave resonator ($Q \\sim 10^5$, $\\omega_r/2\\pi \\sim 5\\,\\text{GHz}$) extends the effective memory time to microseconds, bringing both signatures within reach of current superconducting circuit technology.\n\\bigskip\\noindent\\textbf{Keywords:} Non-Markovian dynamics; Cross-time memory kernels; Macroscopic quantum tunneling; Josephson junctions; Switching-time distribution; Caldeira--Leggett model; Volterra integro-differential equations; Bath correlation spectroscopy","manuscriptTitle":"Cross-Time Memory Kernelsin Macroscopic Quantum TunnelingNon-Markovian Signatures in Josephson Junctions","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2026-03-26 18:05:50","doi":"10.21203/rs.3.rs-9103716/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"decision","content":"Revision requested","date":"2026-05-18T11:18:11+00:00","index":"","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2026-05-03T20:23:03+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2026-04-21T15:14:29+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"315786614050666456824334260111436842979","date":"2026-04-20T16:02:45+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"190622146703728352148864541904869556401","date":"2026-04-14T08:37:37+00:00","index":"hide","fulltext":""},{"type":"reviewersInvited","content":"","date":"2026-03-24T16:15:33+00:00","index":"","fulltext":""},{"type":"editorInvited","content":"","date":"2026-03-24T12:29:17+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2026-03-24T09:31:38+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2026-03-23T15:20:55+00:00","index":"","fulltext":""},{"type":"submitted","content":"Discover Quantum Science","date":"2026-03-23T15:01:41+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"discover-quantum-science","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"","sideBox":"Learn more about [Discover Quantum Science](https://link.springer.com/journal/44464)","snPcode":"44464","submissionUrl":"https://submission.nature.com/new-submission/44464/3","title":"Discover Quantum Science","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Springer Open","inReviewEnabled":true,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"dfa20fbb-dcb9-49f8-9ac5-a48ddbeeab85","owner":[],"postedDate":"March 26th, 2026","published":true,"recentEditorialEvents":[{"type":"decision","content":"Revision requested","date":"2026-05-18T11:18:11+00:00","index":"","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2026-05-03T20:23:03+00:00","index":86,"fulltext":""}],"rejectedJournal":[],"revision":"","amendment":"","status":"in-revision","subjectAreas":[],"tags":[],"updatedAt":"2026-05-18T11:24:19+00:00","versionOfRecord":[],"versionCreatedAt":"2026-03-26 18:05:50","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-9103716","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-9103716","identity":"rs-9103716","version":["v1"]},"buildId":"XKTyCvWXoU3ODBz1xrDgd","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}