Spatio-Temporal Structure of an Effective Qubit Hamiltonian: Diurnal Phase \(\phi(t)\) and Thermal Lag \(\delta_k\) as a Slow Driver (v4.7)

This preprint proposes an operational extension of effective single-qubit Hamiltonian modeling for superconducting platforms, motivated by the possibility of slow, repeatable modulations correlated with a daily cycle. We introduce: - a diurnal phase coordinate \(\phi(t)\in[0,1)\cong\mathbb{S}^1\) (a \(U(1)\) cyclic phase used as a regressor), and - a qubit-specific thermal lag \(\delta_k\) (in radians) that captures qubit-dependent phase delays across a chip/package. The slow modulation is written as an effective \(\mathfrak{su}(2)\) driver added to each qubit Hamiltonian, allowing both longitudinal and optional transverse components. We also provide an operational estimation rule for \(\delta_k\) from first-harmonic fits of drift observables, and we outline a deterministic correction strategy formulated as control-plane feedforward updates (e.g., detuning compensation and frame tracking). A time-ordered formal expression for the correction evolution is included for completeness. This work is a control/identification model intended to support reproducible analysis and scheduling/correction workflows. It does not propose new physical laws and does not claim experimental validation in this manuscript; the included plot is illustrative. Keywords: superconducting qubits, drift modeling, diurnal phase, thermal lag, effective Hamiltonian, feedforward correction, calibration.