The Critical Damping Boundary in a Driven Dephasing Qubit: A Lindblad Testbed for Symmetrical Convergence
Christensen, Nate
Abstract
This work served as a testbed for the SymC critical-damping boundary across the classical–quantum transition using Lindblad dynamics. Its central results are subsumed, generalized, and continued by Structural Constraints from Critical Damping in Open Quantum Field Theories, which provides the full Schwinger–Keldysh and field-theoretic foundation. Version 4 strengthens the manuscript by replacing the earlier heuristic exceptional-point claim with a rigorous eigenanalysis of the Bloch generator and its transverse-mode reduction, including an explicit proof of the EP₂ at Γφ = 2Ω. It also introduces a fully reproducible numerical framework based on event-detected settling times and eigenvalue-trajectory sweeps, resolving the finite-time χ_opt < 1 behavior and sharpening the experimental falsification criteria. ___________ The critical damping boundary χ = Γ/(2|Ω|) = 1 marks a second-order exceptional point in open quantum systems governed by Lindblad dynamics. At this boundary, the generator acquires degenerate poles with Jordan-block structure, the impulse kernel transitions from oscillatory to overdamped form, and observable moments achieve the fastest monotone relaxation. This work provides explicit reduction from Bloch–Lindblad dynamics to canonical second-order form, resolves the apparent discrepancy between the analytic boundary (χ = 1) and finite-time metric optima (χ ≈ 0.8), and demonstrates persistence of the boundary under generalization to higher-order and non-Markovian systems. A falsification program is articulated for circuit QED, trapped-ion, and optomechanical platforms, achieving precision Δχ ≈ 0.02 within current technology. Lindblad dynamics are identified as a quantum-level testbed for the broader Symmetrical Convergence (SymC) framework, with cross-scale inheritance and complex-system validation detailed in a companion supplement.