A New Horizon in Open Quantum Systems: The Phase-Dependent Jump Rate
Saadat Samadi Dinani
We propose that the quantum-jump (decay) rate of an open quantum system can depend on the relative phase δ = θ − φ between the system coherence and a reference oscillation, taking the form Γ(δ) = Γ₀ exp(α cos δ) ≈ Γ₀[1 + α cos δ]. The resulting distribution of jump phases is a von Mises distribution whose first Fourier coefficient is M₁ = I₁(α)/I₀(α) ≈ α/2. Standard Lindblad theory employs a constant rate γ₀; this work replaces it with a phase-dependent rate inside the Lindblad dissipator. The operational definitions are explicit: θ = arg ρ_eg is the phase of the system coherence in a fixed reference frame, and φ is the phase of a classical reference oscillation (a drive tone or a phase-lockable bath mode). The relative phase δ is therefore defined only when such a reference exists — pure Fock-state (photon or phonon number) jumps carry no phase information and cannot test the hypothesis. A two-dimensional metric on the torus (θ, φ), g = [[1, −cos δ], [−cos δ, 1]], is offered solely as geometric motivation for the cos δ form. Its Hessian is singular at δ = nπ, but this singularity does not by itself imply an enhanced decay rate, and it cannot select the sign of α. The step from "Legendre failure" to "rate modulation" is an explicit postulate, not a derivation. This work does not claim to solve the measurement problem. A reproducible injection–recovery test with null controls (4000 trajectories per replicate, seed 2026) recovers injected values of α to within statistical error. For the linear law, the estimator α̂ = 2⟨cos δ⟩ is exactly unbiased with standard error √(2/N); for the exponential (von Mises) law, a maximum-likelihood estimator is obtained by solving M₁ = I₁(α)/I₀(α). Under the null (α = 0), the maximum |M₁| observed across 1500 independent replicates is 0.046, with 95th and 99th percentiles of 0.027 and 0.035. Power analysis indicates that a 3σ detection requires N ≈ 2(3/α)² jumps and a 5σ detection requires N ≈ 2(5/α)² jumps. These simulations validate only the statistical estimator: because α was injected by construction, they are not evidence for the physical hypothesis. The manuscript states the platform requirements for a real test (a driven qubit or oscillator with an explicit classical reference phase, measurable system phase from continuous I/Q records, and trajectory-resolved jump detection), the pre-registration requirements, the null controls, and the rival explanations that must be excluded (phase-dependent detection efficiency, ordinary drive-phase dependence, population-dependent rates, and intrinsic heterodyne detector phase response). No experimental result is claimed. The link between the singular metric and the rate modulation is postulated rather than derived; the phases θ and φ must be tied to a concrete Hamiltonian and reference in each physical system; and the sign of α remains a free parameter of the hypothesis. Keywords: open quantum systems; quantum jumps; phase-dependent decay; von Mises distribution; Lindblad equation; quantum trajectories; injection–recovery; null controls; estimator validation
•Jul 30, 2026•0 citations