Energy-Balance Manifold for Coherence Stabilization and Dynamical Regime Separation in Gaussian-Coupled Qubit Systems

We introduce a theoretical and computational framework in which the coherence of a two-level quantum system interacting with a radial Gaussian field is governed by an intrinsic energy-equilibrium condition between gradient and mass-like contributions. Analytical evaluation of the integrated field energies reveals a stable energy-balance manifold, defined by a log-linear relation between the geometric parameter and the effective coupling parameter . Deviations from this manifold, quantified by a logarithmic energy imbalance, correlate with predictable coherence suppression across more than 40,000 numerical parameter evaluations. Beyond rate suppression, we show that the energy-balance condition is associated with a qualitative change in dynamical behaviour. Time-resolved simulations of Ramsey and echo coherence reveal that near the manifold, phase fluctuations remain confined and exhibit non-Markovian short-time dynamics, while deviations induce rapidly mixing, Markovian decay. Off-manifold dynamics is quantitatively reproduced by an effective telegraph-noise reduction, consistent with the energy-derived dephasing rates. The framework is supported by analytical scaling arguments, large-scale numerical scans, and open-system modeling. Its dimensionless structure makes it directly applicable to superconducting qubits, cavity-QED systems, and bosonic architectures. A complete reproducible package, including analytical derivations, numerical code, and datasets, is provided to facilitate experimental validation.