Extend the renewal model to correlated TLS reconfiguration intervals

Extend the Prabhakar quantum-renewal transmon model to allow correlations between successive TLS reconfiguration intervals, which are assumed to be independent in the present renewal formulation.

Background

The transverse amorphous TLS environment is modeled as a renewal process with independently and identically distributed waiting intervals governed by a Prabhakar law. This assumption enables the exact chronological-history expansion, Volterra equation, kernel–resolvent representation, and directional asymptotic analysis.

The conclusion explicitly identifies correlations between successive reconfiguration intervals as an extension beyond the present model. Incorporating such correlations would be needed to describe environments with memory extending beyond the one-interval renewal statistics.

References

Correlations between successive TLS reconfiguration intervals remain an open extension beyond the present renewal model.

— 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  (2609.37270 - Erdoğan et al., 29 Sep 2026) in Conclusion

The collective ansatz restricts the achievable Kraus operators, and although the renewal subfamily is characterized exactly, the non-renewal case remains open.

— Memory Separations from a Collective-Spin Quantum Register  (2610.08038 - Slim, 6 Oct 2026) in Section Discussion