We introduce a dimensionless dynamical growth parameter, denoted by Γ, designed to quantify the balance between coherent energy accumulation and decoherence time in physical systems. The parameter is defined operationally as the ratio between coherently accumulated energy and a critical energy scale associated with decoherence, ensuring that Γ is non-fundamental and directly linked to measurable quantities. The framework is applied to muons in the kinetic energy range 5–20 MeV, where Γ is shown to naturally cross a coherence threshold without invoking new interactions or modifications of established physical laws. As a minimal supporting example, simple atomic systems (H and He) are discussed to illustrate the generality of the approach.
We introduce a dimensionless dynamical growth parameter, denoted by Γ, designed to quantify the balance between coherent energy accumulation and decoherence time in physical systems. The parameter is defined operationally as the ratio between coherently accumulated energy and a critical energy scale associated with decoherence, ensuring that Γ is non-fundamental and directly linked to measurable quantities. The framework is applied to muons in the kinetic energy range 5–20 MeV, where Γ is shown to naturally cross a coherence threshold without invoking new interactions or modifications of established physical laws. As a minimal supporting example, simple atomic systems (H and He) are discussed to illustrate the generality of the approach.
This work presents the first empirical confirmation of the Static Vibrational Reality (SVR) coherence law within a fully quantum system.By reanalyzing experimental data from Rydberg-atom superradiance, we demonstrate that both the buildup and decay of coherence obey the same nonlinear scaling relation.The characteristic energy–time exponent γ≈1.9 remains invariant across the growth and relaxation phases, confirming a cyclic symmetry in quantum coherence dynamics. These results reveal that quantum amplification and decoherence are not distinct phenomena but complementary phases of a single self-regulating process.Within the SVR framework, time emerges as a phase projection of coherent energy, establishing a direct physical link between quantum reversibility and macroscopic irreversibility.The findings identify coherence as a conserved, cyclic quantity and provide a unifying bridge between quantum and classical descriptions of reality.
This work introduces a minimal and operational framework for describing decoherence in open quantum systems as a finite-time process. Rather than proposing a new dynamical theory or modifying the axioms of quantum mechanics, the article introduces a bounded, causal, and dimensionless scalar quantity — a local temporal coherence field C(x,t), designed to diagnose the persistence of temporal correlations over a finite causal window. The coherence field is constructed from experimentally accessible observables or reduced-state quantities via a kernel-weighted causal average. It does not represent a new physical degree of freedom and does not introduce additional equations of motion. Instead, it provides a compact diagnostic layer that makes the finite-time structure of coherence explicit, complementing standard descriptions based on memory kernels, time-dependent generators, and Lindblad master equations. The framework is shown to interface naturally with non-Markovian dynamics, coherence-weighted decoherence processes, and effective decay rates, while remaining consistent with standard GKSL structures in the appropriate limits. Its scope, limitations, and relation to existing non-Markovianity measures are explicitly discussed. The coherence-field perspective is intended as an operational and experimentally falsifiable diagnostic tool, applicable across a range of contemporary platforms where finite-time coherence effects are relevant (e.g. superconducting circuits, hybrid light–matter systems, and driven non-equilibrium regimes).This article forms part of the broader Ranesis conceptual framework, which investigates the role of finite-time persistence, coherence, and temporal organization across physical and informational systems. Within that context, the present work constitutes a self-contained and domain-specific application to open quantum systems. No assumptions, postulates, or formal structures from the broader framework are required to read or validate the results presented here.
Decoherence is universally described by a single parameter, gamma, which quantifies the rate at which a quantum system loses its phase coherence to its environment. In practice, however, the decoherence rate depends on the specific microscopic configuration of the system, on the spatial mode of the qubits, and on time‑dependent fluctuations of the surrounding bath. This paper introduces the concept of a decoherence landscape, denoted Gamma(x,t), which captures the spatial and temporal variation of the effective decoherence rate across a quantum processor. By treating Gamma(x,t) as a field over the device architecture, we can identify distinct stability regions, characterize phase transitions between coherent and incoherent behavior, and derive design principles that enhance overall robustness. The decoherence landscape framework offers a unified approach to quantify stability, guides error‑mitigation strategies, and reveals hidden regularities that could pave the way for Nobel‑level insights into the fundamental limits of quantum coherence.
Abstract Understanding thermalization and irreversibility in open quantum systems requires char-acterizing the competition between coherent unitary dynamics and dissipative environmen-tal interactions. In this work, we present a systematic numerical study of thermalization dynamics in a two-qubit open quantum system governed by a completely positive and trace-preserving Lindblad master equation. The coherent evolution rate is controlled by a real scaling parameter α multiplying the Hamiltonian commutator, while decoherence is indepen-dently controlled by a dephasing rate γ . Although such a scaling of coherent dynamics can be absorbed into a rescaling of time in isolated systems, it becomes physically meaningful in open systems where decoherence introduces an absolute timescale. We investigate how the relative strength of coherent evolution and decoherence influences observable dynamics, purity decay, entropy production, and thermalization times. Using robust local and two-site observables, we show that varying α at fixed γ produces distinct transient trajectories, even though all evolutions converge to the same steady state. We further define an operational thermalization time τ ( γ, α ) based on a purity threshold and map the resulting thermalization-time surface across a broad parameter range. Increasing α generally accelerates oscillatory dynamics and modifies the approach to equilibrium, leading to measurable shifts in thermalization times without altering asymptotic states. These findings provide a clear and physically consistent characterization of how Hamil-tonian strength and decoherence rate jointly determine thermalization behavior in open quantum systems. The framework offers a practical parameterization for numerical mod-eling and experimental studies of coherent–dissipative competition in quantum information processing, quantum control, and open-system dynamics.
Substrate framework's energy-eigenstate decoherence formula γeff = (ΔE/MPc2)2 × νP [1] depends on the energy gap between superposed states, not on cosmological distance directly. But typical ΔE values for thermal modes, particle physics processes, and inflaton field fluctuations are functions of cosmic energy density, which evolves dramatically over cosmic history. This paper develops the cosmological evolution of substrate intrinsic decoherence across the principal epochs: • Planck era (t ~ 10−44 s): Substrate framework breaks down; γ formula not applicable. • Inflation era (ΔE ~ 1016 GeV): γ ~ 1037 Hz. Catastrophically fast decoherence drives primordial perturbation classicalization — providing the microscopic mechanism for the well-known but mechanistically unexplained quantum-to-classical transition of cosmological perturbations. • EW epoch (ΔE ~ 100 GeV): γ ~ 109 Hz. Coherence time τ ~ ns; particle physics processes decohere rapidly. • QCD epoch (ΔE ~ 100 MeV): γ ~ 103 Hz. τ ~ ms. • Nucleosynthesis (ΔE ~ MeV): γ ~ 0.1 Hz. τ ~ 10 s. • Recombination (ΔE ~ 0.3 eV): γ ~ 10−15 Hz. τ ~ 30 Myr, longer than the age of the universe at that time — the threshold at which the universe becomes capable of sustaining cosmologically long quantum coherence. • Present era (ΔE ~ kBTCMB ~ 0.2 meV): γ ~ 10−21 Hz. τ ~ 30 Gyr, longer than the current age of the universe. Coherent quantum systems can persist for cosmological timescales. • de Sitter future: Floor of γ set by dark energy; in the limit, decoherence approaches a constant minimum tied to the cosmological constant. Three principal results: (i) The decoherence rate has dropped by ~58 orders of magnitude over cosmic history, from γ ~ 1037 Hz at inflation to γ ~ 10−21 Hz today. The universe has become exponentially more capable of sustaining coherent quantum behavior as it has cooled. (ii) Coherent quantum behavior is a late-universe phenomenon. Modern quantum-mechanical experiments (atom interferometry, molecular interferometry, atomic clocks, B-meson oscillations) require a low-energy-density universe to operate. They could not have been performed in the radiation-dominated era because thermal energies were too high. (iii) Substrate framework provides a microscopic mechanism for primordial perturbation classicalization. Inflaton field quantum fluctuations decohered at γ ~ 1037 Hz during inflation, becoming classical perturbations that seeded the large-scale structure observed today. This resolves a long-standing puzzle in cosmology, where the quantum-to-classical transition is traditionally treated as a black box. Additionally, the cosmological floor on momentum uncertainty Δpmin ≥ ℏH(t)/c evolved from Δpmin ~ MPc at Planck era to Δpmin ~ 10−61 kg·m/s today — a quantum bound that has weakened by ~60 orders of magnitude. In the early universe, quantum uncertainty operated at vastly different scales than today. These results imply that the substrate framework's intrinsic decoherence sector is fundamentally a cosmological history sector: the framework's quantum-mechanical behavior changes character with cosmic epoch. Quantum coherence is not a universal property but rather a feature of low-energy-density universes. The framework's testable predictions in the modern era (thermal molecular interferometry, atomic clocks) are made possible by the universe having sufficiently cooled. Section II clarifies what does and doesn't depend on cosmic time. Section III develops the cosmological floor evolution. Section IV develops the decoherence rate across cosmic history with a master table. Section V addresses the early universe's rapid classicalization. Section VI addresses the inflation era specifically and primordial perturbations. Section VII addresses the present era. Section VIII addresses the de Sitter future. Section IX synthesizes the cross-epoch comparison of quantum properties. Section X concludes. Keywords: substrate theory; cosmological decoherence; primordial perturbations; inflation; quantum-to-classical transition; cosmological floor; energy-eigenstate formula; cosmic evolution of quantum capacity.
We investigate a candidate, scale-free coherence invariantΠ ≡ℏ τmd2 ,built from an inertial (or effective modal) mass m, a characteristic coherence or separationlength d, and a coherence or correlation time τ . The original motivation was the possibilitythat a single dimensionless parameter might organize coherence behaviour across a widerange of physical regimes. In this work we take a more modest and technically explicitposition.First, P we present the theoretical framework that motivates Π: a phase–ledger C(t) =i Φi(t) whose conservation, ˙C = 0, leads to local quadratic invariant manifolds in native,dimensionless coordinates. We show, via Buckingham–Π analysis, that for systems whoserelevant variables are (m, d, τ ; ℏ) there is a unique dimensionless combination of this form.Second, we test the coherence invariant hypothesis on a set of heterogeneous butconcrete examples drawn from nine “rungs”: quantum decoherence and matter-waveinterferometry, nonlocal/Bell-type experiments, near- and far-field electromagnetism,astrophysical lines, condensates, cosmic expansion, and dynamic “poke-and-return” motionin atom interferometers and Bose–Einstein condensates. The goal is not to claim a fullyestablished universal law, but to examine where the proposed invariant is (and is not)consistent with data under clearly stated choices of (m, d, τ ).Third, we confront a key limitation: in many platforms there are multiple, physicallyplausible definitions of d and τ . Different choices can shift Π by many orders of magnitude.We therefore emphasize the risk of post-hoc scale selection (“curve fitting”) and propose acanonical scale protocol for future tests: (i) state all plausible definitions of (m, d, τ ) for agiven dataset, (ii) compute Π for each, and (iii) treat the choice that minimizes deviationfrom a hypothesized invariant surface as an empirical question, not a built-in assumption.With these caveats, we find that:• Near-field matter-wave interferometers analysed using the Talbot time as the native τadmit a natural mapping in which an onset band in Π near O(10−1) appears plausible.• Cold-atom and BEC transport experiments, when expressed in terms of their trapscales and transport times, yield very large Π (deep coherence), consistent with theintuitive classification of strongly regulated motion.• In other domains (Bell tests, far-field EM, astrophysical lines, cosmology) the presentevidence is mixed or inconclusive: sensible alternative choices of (m, d, τ ) cannot yetbe ruled out, and the existence of a single cross-domain onset constant is thereforeunproven.iThe main contribution of this paper is thus not a final claim of universality but aclearly defined hypothesis, a normalization and falsifiability protocol, and a set of workedexamples illustrating both the promise and the pitfalls of coherence invariants acrossphysical scales. We highlight specific experiments and re-analyses—especially in matterwaveinterferometry, collisional decoherence, condensates, and atom interferometer/BECdynamics—that could rapidly confirm or falsify key aspects of the framework.Contents