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 (σy,σz) subspace supporting directional transfer between coherence and longitudinal polarization; σx polarization is renewal-insensitive. For heavy-tailed waiting times with 0<α<1, branch-cut analysis gives a generic t−α storage tail in longitudinal polarization generated from initial coherence and O(t−1−α) reverse transfer; constant-rate Poisson renewal yields pole-generated exponential decay. Independent zero-temperature relaxation at finite T1 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-T1 tests. Both Poisson references yield larger evaluated finite-window peaks. Disorder-motivated renewal memory reshapes transmon decoherence selectively by state and direction.
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BibTeX
@misc{erdogan2026directional,
title = {{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}},
author = {Ruha Uğraş Erdoğan and Ferit Acar Savacı},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.37270},
eprint = {2609.37270},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.37270},
}
RIS
TY - UNPB
TI - 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
AU - Ruha Uğraş Erdoğan
AU - Ferit Acar Savacı
PY - 2026
DA - 2026/09/29
PB - arXiv
DO - 10.48550/arxiv.2609.37270
UR - https://arxiv.org/abs/2609.37270
AB - 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 (σ_y,σ_z) subspace supporting directional transfer between coherence and longitudinal polarization; σ_x polarization is renewal-insensitive. For heavy-tailed waiting times with 0<α<1, branch-cut analysis gives a generic t^−α storage tail in longitudinal polarization generated from initial coherence and O(t^−1−α) 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.
ER -