Directional transfer from coherence to longitudinal polarization and algebraic storage in a transmon with Markovian dephasing and a glassy environment: A non-Markovian fractional renewal model

Abstract:We develop a completely positive and trace-preserving non-Markovian transmon model with longitudinal Markovian dephasing and transverse renewal events motivated by a glassy two-level-system environment. A microscopic Hamiltonian identifies coupling subspaces; a normalized Prabhakar waiting-time law phenomenologically coarse grains slow defect reconfigurations. Forward chronological renewal histories yield an exact map-level Volterra equation, a noncommuting kernel--resolvent master equation, and an equivalent drift-conjugated Caputo-type representation with its required initial-value term. Without energy relaxation, Pauli-space dynamics splits into two one-dimensional subspaces and a coupled $(\sigma_y,\sigma_z)$ subspace supporting directional transfer between coherence and longitudinal polarization; $\sigma_x$ polarization is renewal-insensitive. For heavy-tailed waiting times with $0<\alpha<1$, branch-cut analysis gives a generic $t^{-\alpha}$ storage tail in longitudinal polarization generated from initial coherence and $O(t^{-1-\alpha})$ reverse transfer; constant-rate Poisson renewal yields pole-generated exponential decay. Independent zero-temperature relaxation at finite $T_1$ exponentially cuts off these tails when its rate is below twice the pure-dephasing rate. We compare independent inverse-Laplace reconstructions of the waiting-time density, memory kernel, and selected qubit-response components to assess numerical accuracy. For the studied parameters, Prabhakar renewal gives larger forward-transfer magnitudes at the prescribed readout than both a scale-matched constant-rate Poisson reference and an inhomogeneous Poisson reference matching the full expected-count profile, including finite-$T_1$ tests. Both Poisson references yield larger evaluated finite-window peaks. Disorder-motivated renewal memory reshapes transmon decoherence selectively by state and direction.

38 pages (main text and appendices), 10 figures. Submitted to Physical Review A on the 28th of September 2026

arXiv:2609.37270 [quant-ph]

(or arXiv:2609.37270v1 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2609.37270 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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.