The phenomenological decoherence principle introduced in Ryabokon (2026a) expresses coherence loss as an exponential of the integral of the squared effective field F. In this paper we analyze the statistical foundations of stretched-exponential decay, which arises when F possesses scale-invariant (fractal) statistics. Starting from a power-law spectrum Φ(k) ∝ k^{-p}, we derive explicit relations between the spectral index p and the stretched-exponential exponent β. For Gaussian fluctuations we obtain: β = p-1 for the field itself, and β = p-2 for integrated quantities (e.g., wave phase). The domain of validity and the role of non-Gaussian statistics are discussed. This publication is part of a broader conceptual program aimed at providing a unified phenomenological description of decoherence and attenuation processes. The framework is fully consistent with standard quantum mechanics and should be viewed as an organizing perspective rather than a proposal of new dynamics.
The phenomenological decoherence principle introduced in Ryabokon (2026a) expresses coherence loss as an exponential of the integral of the squared effective field F. In this paper we analyze the statistical foundations of stretched-exponential decay, which arises when F possesses scale-invariant (fractal) statistics. Starting from a power-law spectrum Φ(k) ∝ k^{-p}, we derive explicit relations between the spectral index p and the stretched-exponential exponent β. For Gaussian fluctuations we obtain: β = p-1 for the field itself, and β = p-2 for integrated quantities (e.g., wave phase). The domain of validity and the role of non-Gaussian statistics are discussed. This publication is part of a broader conceptual program aimed at providing a unified phenomenological description of decoherence and attenuation processes. The framework is fully consistent with standard quantum mechanics and should be viewed as an organizing perspective rather than a proposal of new dynamics.
This is the second paper in a series on the phenomenological principle of decoherence. The first paper, "Phenomenological Principle of Decoherence Based on the Integral Impact of Environmental Fields" (Ryabokon, 2026), is available at DOI: 10.5281/zenodo.18640591. In the present work, we elaborate on the physical meaning and possible realizations of the effective environmental field F(x), which plays a central role in the decoherence principle: C/C0 = exp(-α ∫_γ F²(x) dx). While the original formulation allowed F to represent any local interaction, here we show that in many realistic environments F is best described as a random field with fractal (scale-invariant) correlations. For such fields, the integral ∫ F² dx scales with the system size L as L^β, leading to a stretched-exponential decay of coherence: C/C0 = exp(-α' L^β). We derive the relation between the exponent β and the spectral index p of the field: β = p-2 (valid for 1 < p < 3). This result is supported by known examples from atmospheric optics (Kolmogorov turbulence, β = 5/3), biological tissues, and cosmological density fluctuations. We also discuss how to experimentally determine β and outline the limits of applicability of the proposed scaling. The framework does not modify the original principle but extends its domain to a broad class of natural and artificial media, offering a unified language for decoherence in complex environments.This publication is part of a broader conceptual program aimed at providing a unified phenomenological description of decoherence and attenuation processes. The framework is fully consistent with standard quantum mechanics and should be viewed as an organizing perspective rather than a proposal of new dynamics.
This work proposes a phenomenological formulation of a decoherence principle that relates the degree of suppression of quantum coherence to the integral of the squared effective environmental field in the physical systems and experimental configurations analyzed in this paper. The environment is treated as a set of effective physical influences relevant to a specific experimental or physical configuration and acting on the system. The applicability of the proposed principle is analyzed using seventeen experiments and observations spanning microscopic, mesoscopic, macroscopic, and cosmological scales. Seven key experiments are analyzed quantitatively and in detail, while the remaining ones are presented as supporting the broad applicability of the proposed phenomenological approach. This publication is part of a broader conceptual program aimed at providing a unified phenomenological description of decoherence and attenuation processes. The framework is fully consistent with standard quantum mechanics and should be viewed as an organizing perspective rather than a proposal of new dynamics.
We report evidence consistent with non-exponential decoherence in superconducting transmon qubits. Ramsey interferometry data from five qubits on IBM Quantum hardware show that a stretched-exponential model f(t) = exp(-(t/T2 ) beta) fits the observed decay better than the standard exponential (beta = 1). On our primary qubit (Q0), we measure beta = 2.06 with R2 = 0.9964 versus R2 = 0.9586 for the exponential, with Bayesian Information Criterion favoring the stretched model by 46 units. While non-exponential decay in superconducting qubits has been previously observed in the context of 1/f noise [4], the present work provides a systematic multi-qubit characterization with a fully reproducible protocol and proposes a falsifiable geometry-dependent prediction (RAB != 1) that distinguishes this framework from collapse-model alternatives.
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.
Abstract We identify and investigate the origin and nature of the transition between Gaussian and exponential forms of decoherence: the decoherence factor (that controls the time dependence of the off-diagonal terms of the density matrix expressed in the pointer basis representation) is the convolution of the Fourier transforms of the spectral density and of the overlap (between the eigenstates the environment with and without couplings to the system). Spectral density alone tends to lead to the (approximately) Gaussian decay of coherence while the overlap alone results in a (largely) exponential decay. We show that these two contributions combine as a convolution, their relative importance controlled by the strength of the system-environment coupling. The resulting decoherence factor in the strong and weak coupling limits leads to predominantly Gaussian or exponential decay, respectively, as is demonstrated with two paradigmatic examples of decoherence—a spin-bath model and the quantum Brownian motion.
This explanation is based on the phenomenological decoherence principle presented in https://doi.org/10.5281/zenodo.18640591. According to this principle, the probability of maintaining coherence (e.g., the absence of scattering) is given by an exponential of the integral of the squared effective environmental field: C = C_0 exp(-alpha integral F^2 dx). We show how this principle, combined with quantum mechanics, naturally yields the famous Rayleigh law (λ^(-4)) that explains the color of the sky. We present an alternative derivation of the Rayleigh scattering cross section starting from a microscopic model of light scattering by independent molecules. The exponential attenuation law (Bouguer–Lambert–Beer law) is linked to the sum of squared scattering amplitudes of individual particles, which follows directly from the phenomenological decoherence principle. Using a three-dimensional harmonic oscillator as a model of a molecule, we compute the elastic photon scattering amplitude to second order in perturbation theory within the dipole approximation. The resulting cross section exhibits the characteristic ω^4 dependence, directly accounting for the blue color of the sky and the redness of the Sun at sunset. No empirical data are used; all results follow from first principles of quantum mechanics and the proposed decoherence principle. This publication is part of a broader conceptual program aimed at providing a unified phenomenological description of decoherence and attenuation processes. The framework is fully consistent with standard quantum mechanics and should be viewed as an organizing perspective rather than a proposal of new dynamics.