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Search Results (421)

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21 pages, 4056 KB  
Article
Optimizing Red–Blue LED Light Recipes for Improved Biomass Production and Nutritional Quality of Purple Celery in Plant Factory Cultivation
by Wei Lu, Chan Zhang, Chunlei Zhu, Kexin Guo, Jiuhui Tang, Yuansheng Bao, Chi Qin, Zijing Luo, Mingman Xu, Chengyao Jiang, Mengyao Li, Yangxia Zheng, Sen Wang and Naimin Kong
Agriculture 2026, 16(16), 1768; https://doi.org/10.3390/agriculture16161768 - 18 Aug 2026
Viewed by 214
Abstract
Purple celery (Apium graveolens L.) is a high-value functional vegetable rich in anthocyanins, but achieving a balanced optimization between biomass accumulation and nutritional quality in plant factories remains challenging due to species-specific spectral trade-offs, and current research lacks integrated light recipes that [...] Read more.
Purple celery (Apium graveolens L.) is a high-value functional vegetable rich in anthocyanins, but achieving a balanced optimization between biomass accumulation and nutritional quality in plant factories remains challenging due to species-specific spectral trade-offs, and current research lacks integrated light recipes that simultaneously optimize photosynthetic efficiency, antioxidant defenses, and functional quality while suppressing nitrate accumulation. This study evaluated five LED treatments over 30 days: white light (CK), monochromatic red (R), and red-to-blue photon flux density ratios of 5:5, 7:3, and 8:2. Red light induced stem elongation but suppressed root development. Conversely, 8R2B delivered the best performance, significantly elevating leaf, petiole, root, and total fresh biomass and increasing total dry weight by 68.8% over CK. It also markedly enhanced chlorophyll a, b, total chlorophyll, and carotenoids, as well as improved PSII quantum yield (YII), photochemical quenching (qP), and electron transport rate (ETR), while reducing non-photochemical heat dissipation (NPQ) by 61.0%, indicating superior light-use efficiency. Furthermore, 8R2B upregulated CAT and POD activities promoted soluble sugars (up 688.4% in leaves), soluble proteins, and ascorbic acid accumulation, yet reduced leaf nitrate by 28.5%. Principal component analysis confirmed 8R2B as the most effective formulation across all growth, photochemical, defense, and quality traits. These findings provide a novel, evidence-based 8:2 red-to-blue LED light recipe for high-yield, high-quality, and commercially viable purple celery production in controlled environment agriculture. Full article
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17 pages, 1372 KB  
Article
A Physics-Informed Neural Network Scheme for Shortcuts to Adiabaticity in Three-Level Non-Hermitian Quantum Systems
by Ming Liu, Fengxiao Huang, Siqi Zhang, Feng Yang, Wei Zhao, Junling Liu and Hong Li
Entropy 2026, 28(8), 897; https://doi.org/10.3390/e28080897 - 10 Aug 2026
Viewed by 178
Abstract
We propose a physics-informed neural network (PINN) scheme for designing shortcuts to adiabaticity in a three-level non-Hermitian quantum system. The PINN is used to solve an inverse control problem in which the state amplitudes and the auxiliary driving field are learned simultaneously from [...] Read more.
We propose a physics-informed neural network (PINN) scheme for designing shortcuts to adiabaticity in a three-level non-Hermitian quantum system. The PINN is used to solve an inverse control problem in which the state amplitudes and the auxiliary driving field are learned simultaneously from the Schrödinger residual, the initial and target population constraints and a probability conservation constraint on the control pulse. The learned compensation field counteracts the loss of the intermediate state and enables high-fidelity population inversion in an open-system setting. Importantly, the imposed probability conservation is treated as an auxiliary constraint along the learned trajectory rather than as an intrinsic property of the non-Hermitian Hamiltonian. Under this constrained evolution, the Hamiltonian expectation value evaluated on the obtained state remains real within numerical accuracy. Numerical simulations and independent propagation with the fitted control field verify the population inversion and exhibit strong generalization capability over a range of coupling strengths and dissipation rates, as verified by retraining the network independently for each parameter set. The results demonstrate that PINNs provide a flexible inverse design tool for non-Hermitian shortcut to adiabaticity protocols when the governing dynamics and physical constraints are explicitly incorporated into the loss function. Full article
(This article belongs to the Special Issue Quantum Algorithms and Quantum Machine Learning)
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13 pages, 5110 KB  
Article
Research on the Dynamics of Cold Atoms Under Non-Equilibrium Dissipation
by Yifan Gao, Yanhang Chen, Shuyu Dai and Bo Cui
Entropy 2026, 28(8), 890; https://doi.org/10.3390/e28080890 - 7 Aug 2026
Viewed by 245
Abstract
We investigate the dissipative dynamics of a one-dimensional sawtooth-shaped Bose–Hubbard model subjected to an external magnetic flux and staggered single-particle dissipation. By combining the Lindblad master equation with a mean-field decoupling and further reducing the dynamics to an effective three-site model, we derive [...] Read more.
We investigate the dissipative dynamics of a one-dimensional sawtooth-shaped Bose–Hubbard model subjected to an external magnetic flux and staggered single-particle dissipation. By combining the Lindblad master equation with a mean-field decoupling and further reducing the dynamics to an effective three-site model, we derive the nonlinear evolution equations that govern the system. Our results reveal that the magnetic flux, acting through the next-nearest-neighbor hopping, determines the preferential direction of particle flow, while the imbalance in dissipation forces the steady-state population to accumulate at lattice sites with weaker loss. Furthermore, we find that two-particle dissipation accelerates the relaxation process when it becomes negative (i.e., gain), whereas positive two-particle loss suppresses localization. These findings demonstrate that directional localization and relaxation dynamics can be controlled by the sign of the next-nearest-neighbor hopping t′ and the magnetic phase, providing a tunable scheme for engineering dissipative quantum states in optical lattices. Full article
(This article belongs to the Section Non-equilibrium Phenomena)
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19 pages, 2096 KB  
Article
Photoconversion Covers Based on CdSe/CdS-ZnS Quantum Dots Improve Photosynthetic Performance and Vegetative Growth of Tomato Plants (Solanum lycopersicum)
by Denis V. Yanykin, Mark O. Paskhin, Sergey A. Shumeyko, Dmitry A. Zakharov, Grigorii A. Oloviannikov, Nikita S. Parashchuk, Denis N. Chausov, Yurii Trutnev, Sergey V. Gudkov and Valeriy A. Kozlov
AgriEngineering 2026, 8(8), 322; https://doi.org/10.3390/agriengineering8080322 - 3 Aug 2026
Viewed by 356
Abstract
The effect of light spectrum conversion using photoconversion covers (PCCs) containing CdSe/CdS-ZnS quantum dots (PCC-QDs) on the growth and photosynthesis of tomato plants was studied. Luminophore-free covers and covers containing rhodamine B as a luminophore (PCC-RB) were used as reference covers. The obtained [...] Read more.
The effect of light spectrum conversion using photoconversion covers (PCCs) containing CdSe/CdS-ZnS quantum dots (PCC-QDs) on the growth and photosynthesis of tomato plants was studied. Luminophore-free covers and covers containing rhodamine B as a luminophore (PCC-RB) were used as reference covers. The obtained covers had a luminescence maximum in the red region (618 nm for PCC-QDs and 615 nm for PCC-RBs). It was shown that both types of PCC promoted plant growth, with PCC-QDs increasing leaf number by 28% and chlorophyll content by 6%, while PCC-RB enhanced stem length (17%) and leaf number (23%), with no effect on chlorophyll content after a reduction in the thermal dissipation of absorbed light energy and intensifying electron transfer in the photosynthetic electron transport chain, which was accompanied by a 40–50% increase in the hydrogen peroxide content in plant tissues and a 2–3-fold increase in ascorbate peroxidase activity. Light-induced activation of transpiration in PCC plants was found to occur within 1–2 min, while control plants exhibited greater stomatal inertia with a 4–5 min delay in response to light. It is assumed that changes in the light spectrum induced by PCCs led to the optimization of electron transport in chloroplasts, triggering H2O2-mediated activation of gas exchange in leaves. Full article
(This article belongs to the Section Sustainable Bioresource and Bioprocess Engineering)
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29 pages, 2865 KB  
Article
A Pole-Based Approach to Composite Linear Optical Cavities with Internal Dielectric Reflectors
by Vedran Vujnović, Nenad Kralj and Marin Karuza
Photonics 2026, 13(8), 721; https://doi.org/10.3390/photonics13080721 - 30 Jul 2026
Viewed by 356
Abstract
We develop a versatile description of Fabry–Pérot resonators comprising internal dielectric structures, based on transfer matrices and interpreted from a non-Hermitian one-pole self-energy viewpoint. For a two-mirror cavity containing an internal slab of arbitrary thickness and refractive index, we derive closed-form expressions for [...] Read more.
We develop a versatile description of Fabry–Pérot resonators comprising internal dielectric structures, based on transfer matrices and interpreted from a non-Hermitian one-pole self-energy viewpoint. For a two-mirror cavity containing an internal slab of arbitrary thickness and refractive index, we derive closed-form expressions for transmission and identify cavity poles as zeros of the reduced denominator in the complex-frequency plane. For a weak-reflector, we obtain leading-order expressions for the pole shifts of individual modes and show that the resulting mode pulling and linewidth change are, respectively, governed by the imaginary and real parts of a single complex quantity formed by the coherent sum of two mirror-side scattering paths. These expressions provide placement criteria for dispersive or dissipative operation and support practical workflows for extracting weak-reflector parameters from measured resonance traces, predicting slab-modified cavity spectra from the empty cavity calibration, and designing doubly resonant cavities with fine constraints on slab position. We extend the consideration to multiple reflectors, with emphasis on two-membrane and three-mirror geometries, relevant to coupled filter cavities and membrane-in-the-middle architectures. The coupled-pole parametrization relates these configurations, providing a compact framework for the analysis and design of composite Fabry–Pérot elements for precision filtering and quantum-noise shaping in advanced interferometric experiments. Full article
(This article belongs to the Section Optical Interaction Science)
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35 pages, 6620 KB  
Review
Wafer Support Systems (WSSs) as Beam–Matter Interaction Platforms: Electrostatic Chucking, Thermal Transport, Metrology Coupling, Industrial Architectures, and Emerging Semiconductor Platforms
by Abbas Alshehabi, Jaafar Almutawa and Mahmood Abduljabbar Hammad
Quantum Beam Sci. 2026, 10(3), 17; https://doi.org/10.3390/qubs10030017 - 23 Jul 2026
Viewed by 523
Abstract
Wafer support systems (WSSs) are commonly treated as passive mechanical fixtures in semiconductor tools, yet they function in practice as active beam-facing platforms that shape the conditions under which quantum beams interact with wafers. This review re-examines WSSs from a quantum beam science [...] Read more.
Wafer support systems (WSSs) are commonly treated as passive mechanical fixtures in semiconductor tools, yet they function in practice as active beam-facing platforms that shape the conditions under which quantum beams interact with wafers. This review re-examines WSSs from a quantum beam science perspective by integrating beam–matter interaction physics, electrostatic chucking, thermal transport, precision stage dynamics, industrial platform architectures, and beam-coupled metrology within a unified framework. Drawing on academic and industrial sources, the review compares lithography, plasma-processing, deposition, inspection, and metrology environments to show how support-platform design influences stability, heat dissipation, charging behavior, vibration sensitivity, wafer flatness, and defect detectability. Particular emphasis is placed on electrostatic chucks as coupled electrical and thermal interfaces, on precision motion systems as beam-conditioning infrastructure, and on the growing role of support architectures in advanced X-ray, electron-beam, and hybrid metrology workflows. Selected comparative figures are constructed to support cross-platform interpretation. By framing WSSs as beam–matter interaction platforms rather than passive hardware, this review identifies new opportunities for linking beam physics, materials selection, thermal management, and precision engineering in next-generation semiconductor manufacturing and metrology, including emerging smart support architectures with sensing, adaptive control, and data-driven optimization. Full article
(This article belongs to the Section Engineering and Structural Materials)
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19 pages, 1712 KB  
Article
A Husimi Phase-Space Approach to a Driven–Dissipative Quantum Field at Finite Temperature
by Marco A. García-Márquez, Irán Ramos-Prieto, Francisco Soto-Eguibar and Héctor M. Moya-Cessa
Dynamics 2026, 6(3), 26; https://doi.org/10.3390/dynamics6030026 - 23 Jul 2026
Viewed by 437
Abstract
We investigate the dynamics of a driven quantum field coupled to a finite-temperature reservoir. The corresponding master equation is solved using superoperator techniques, yielding an analytical expression for the density operator. To obtain a compact and physically transparent description of the dynamics, we [...] Read more.
We investigate the dynamics of a driven quantum field coupled to a finite-temperature reservoir. The corresponding master equation is solved using superoperator techniques, yielding an analytical expression for the density operator. To obtain a compact and physically transparent description of the dynamics, we adopt a phase-space representation based on the Husimi Q-function. For an initially coherent state, we derive a closed-form Gaussian expression for the Husimi Q-function whose stationary limit corresponds to a displaced thermal state. This approach also enables an analytical study of quantum-interference dynamics for an initial superposition of coherent states. Furthermore, we derive the corresponding Fokker–Planck equation for the Husimi Q-function and obtain closed-form expressions for relevant statistical quantities, including the mean photon number, the photon-number standard deviation, and the Mandel parameter. We also investigate the Wehrl and linear entropies, which quantify the loss of phase-space information and purity induced by the thermal environment. The framework provides a complete analytical characterization of the phase-space dynamics, photon statistics, and entropic properties of driven–dissipative quantum fields while avoiding the explicit manipulation of the density operator. Full article
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26 pages, 1157 KB  
Article
The Measurement Problem in the Thermodynamics of Black Holes
by Jeroen Schoenmaker
Entropy 2026, 28(7), 808; https://doi.org/10.3390/e28070808 - 15 Jul 2026
Viewed by 709
Abstract
This manuscript gives a solution to the black hole information paradox by bringing to the debate a fundamental aspect of information science: the process of measurement by a receiver. Bekenstein and Hawking established the foundations of black hole thermodynamics based on previous works [...] Read more.
This manuscript gives a solution to the black hole information paradox by bringing to the debate a fundamental aspect of information science: the process of measurement by a receiver. Bekenstein and Hawking established the foundations of black hole thermodynamics based on previous works of Brillouin and Szilard on information physics. In this work, we demonstrate that the relation between energy and information established in communication technology by Shannon and Landauer has not been adequately applied to black hole physics. As Landauer states, a computation process is closely akin to a measurement. Our argument is grounded on the physical concepts of measurement, signal-to-noise ratio, energy dissipation during the switching process in computation, and hysteresis loops. We give special attention to the role of noise and energy dissipation in the process of information transmission. We demonstrate that Szilard’s work fails to establish a connection between information and entropy in agreement with the works of Landauer and Shannon. We also demonstrate that a quantum state cannot be directly equivalent to a unit of information. The entropy and temperature attributed to black holes are questioned, and a solution to the black hole information paradox is provided. Similarly to what happens with Maxwell’s demon, the black hole information paradox is “exorcised” once we account for the process of measurement and information processing. Full article
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24 pages, 11385 KB  
Article
Switchable Dissipative Ising Coupling Based on Three-Body Coupling in Magnon Systems
by Xiwen Dou, Zhengyang Zhou and Aixi Chen
Photonics 2026, 13(7), 665; https://doi.org/10.3390/photonics13070665 - 12 Jul 2026
Viewed by 447
Abstract
Magnonic systems present a compelling platform for quantum technology, owing to their strong capacity to form hybrid quantum systems via diverse couplings. To unlock the full potential of these systems, the engineering of flexible coupling between multiple magnon modes is essential. Here, we [...] Read more.
Magnonic systems present a compelling platform for quantum technology, owing to their strong capacity to form hybrid quantum systems via diverse couplings. To unlock the full potential of these systems, the engineering of flexible coupling between multiple magnon modes is essential. Here, we propose a method to realize switchable dissipative Ising coupling in magnon systems, leveraging the three-body coupling among photon, phonon, and magnon. This type of dissipative coupling is a critical component for constructing Ising machines designed to solve complex combinatorial optimization problems. By dynamically tuning the phase of a nonlinear mechanical pump, we demonstrate the realization of both ferromagnetic and antiferromagnetic dissipative interactions. The validity of the scheme is confirmed by numerical simulations, which also demonstrate its robustness against a strong uncontrollable part of dissipation. Our work provides a versatile tool that can facilitate the implementation of magnon-based quantum computing and the exploration of many-body magnon physics. Full article
(This article belongs to the Special Issue Quantum Optics: Communication, Sensing, Computing, and Simulation)
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36 pages, 693 KB  
Article
Evolution of Hypoequilibrium States in Steepest Entropy Ascent Models for Nonequilibrium Quantum Thermodynamics
by Gian Paolo Beretta, Rohit Kishan Ray and Michael R. von Spakovsky
Entropy 2026, 28(7), 772; https://doi.org/10.3390/e28070772 - 7 Jul 2026
Viewed by 336
Abstract
A formal development of the HypoEquilibrium (HE) state concept within the Steepest-Entropy-Ascent Quantum Thermodynamics (SEAQT) framework is presented, emphasizing its rigorous mathematical formulation. Using a general decomposition of the Hilbert space, HE states are defined in operator language and the reduced evolution of [...] Read more.
A formal development of the HypoEquilibrium (HE) state concept within the Steepest-Entropy-Ascent Quantum Thermodynamics (SEAQT) framework is presented, emphasizing its rigorous mathematical formulation. Using a general decomposition of the Hilbert space, HE states are defined in operator language and the reduced evolution of the associated intensive parameters for the regime where the dissipative dynamics commutes with the Hamiltonian is derived. It is proved that the M-th-order HE family (where M is the number of spectral sectors) constitutes an invariant manifold under the SEAQT equation of motion, ensuring that states initially representing a “mixture of canonicals” maintain this structure throughout their evolution. Furthermore, a formal connection is established between the HE ansatz and the rate-controlled constrained equilibrium (RCCE) method, identifying HE variables as constraint potentials. Finally, the model is extended to Non-Hamiltonian SEAQT (NH-SEAQT) interactions to describe thermodynamically consistent energy and entropy exchanges between subsystems and heat baths. This work provides the formal foundation for reduced-order modeling of far-from-equilibrium relaxation and transport processes, and supports a methodology previously applied across various physical and chemical systems. Full article
(This article belongs to the Section Non-equilibrium Phenomena)
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23 pages, 8954 KB  
Article
Strict Time-Resolved Steady States via Affine-Eigenstate Mapping: A Robust Framework for Ultracold Atom–Molecule Dynamics
by Yanhang Chen, Gaoyang Du, Chenglong Yang, Shuyu Dai and Bo Cui
Entropy 2026, 28(7), 752; https://doi.org/10.3390/e28070752 - 1 Jul 2026
Viewed by 410
Abstract
We propose a theoretical framework based on an affine-eigenstate transformation for analyzing ultracold atom–molecule conversion dynamics with particle loss. The transformation maps the mean-field dynamics to an effective two-mode representation in which fixed points, Bloch-sphere trajectories, and linear stability can be examined in [...] Read more.
We propose a theoretical framework based on an affine-eigenstate transformation for analyzing ultracold atom–molecule conversion dynamics with particle loss. The transformation maps the mean-field dynamics to an effective two-mode representation in which fixed points, Bloch-sphere trajectories, and linear stability can be examined in a common set of variables. We give the derivation of the transformed Hamiltonian and specify the invertibility and conjugate-condition requirements under which the mapping is used. Within this representation, we distinguish ordinary, pseudo, and strict self-trapping regimes. The strict regime is associated with the balanced condition S=0 in the transformed variables; in the corresponding linearized dissipative flow, the leading attractor/repeller bifurcation term controlled by SΓ vanishes, explaining the observed robustness against atom- and molecule-loss imbalance. We also introduce von Neumann and linear-entropy diagnostics for future mixed-state or ensemble descriptions in the transformed two-level representation, and we provide an inverse reconstruction procedure for preparing initial states that realize strict self-trapping. Finally, we discuss the limits of the mean-field and Markovian approximations and outline how finite-particle simulations and phase-modulated control protocols could connect this mechanism to decoherence-resilient quantum simulations and information-processing architectures. Full article
(This article belongs to the Special Issue Open Quantum Dynamics in Non-Equilibrium and Complex Systems)
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19 pages, 621 KB  
Article
Zeeman Symmetry Breaking as a Tool for Protecting Quantum Coherence and Purity Against Dephasing in Atomic Hydrogen
by Kamal Berrada and Smail Bougouffa
Symmetry 2026, 18(7), 1086; https://doi.org/10.3390/sym18071086 - 26 Jun 2026
Viewed by 277
Abstract
The hyperfine structure of the hydrogen atom provides a clean, experimentally relevant two-qubit platform in which the coupled electron and proton spins exhibit rich quantum behavior. We investigate the open-system dynamics of this system under the simultaneous influence of the intrinsic hyperfine coupling, [...] Read more.
The hyperfine structure of the hydrogen atom provides a clean, experimentally relevant two-qubit platform in which the coupled electron and proton spins exhibit rich quantum behavior. We investigate the open-system dynamics of this system under the simultaneous influence of the intrinsic hyperfine coupling, an external static magnetic field (via the Zeeman interaction), and local Markovian dephasing noise. Employing the Lindblad master equation, we derive the exact time evolution of the density matrix for general X-shaped initial states and focus on two complementary measures of quantum coherence—the L1-norm coherence CL(t) and the relative entropy of coherence CR(t)—together with the state purity P(t). Numerical results reveal that all three quantities display characteristic damped oscillatory evolution. For a vanishing magnetic field, the decay is relatively rapid and smooth, whereas increasing the proton magnetic parameter markedly raises the oscillation frequency and slows the overall envelope of both coherence and purity. Even under stronger dephasing rates, a suitably chosen external field can substantially postpone the loss of quantum features, acting effectively as a control knob that reshapes the coherent unitary dynamics to counteract dissipative effects. These findings underscore the delicate competition between intrinsic atomic interactions and environmental noise, while offering a practical route for protecting quantum resources in spin-based systems. Our work bridges fundamental atomic physics with resource-theoretic concepts and highlights promising strategies for coherence preservation in realistic, controllable quantum platforms. Full article
(This article belongs to the Section C: Physics)
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41 pages, 24656 KB  
Article
Dynamical Analysis of Fractional Whitham–Broer–Kaup Systems Under Deterministic and Stochastic Effects
by Atef Abdelkader, Maham Munawar, Adil Jhangeer and Mudassar Imran
Fractal Fract. 2026, 10(7), 426; https://doi.org/10.3390/fractalfract10070426 - 24 Jun 2026
Viewed by 360
Abstract
The fractional Whitham–Broer–Kaup model governs nonlinear wave propagation in memory-dependent media, including porous structures, viscoelastic fluids, and irregular seabeds, yet the full dynamical spectrum from quasi-periodicity to deterministic chaos, the role of stochastic forcing, and reliable identification from noisy data remains insufficiently explored, [...] Read more.
The fractional Whitham–Broer–Kaup model governs nonlinear wave propagation in memory-dependent media, including porous structures, viscoelastic fluids, and irregular seabeds, yet the full dynamical spectrum from quasi-periodicity to deterministic chaos, the role of stochastic forcing, and reliable identification from noisy data remains insufficiently explored, particularly how the fractional order β influences these regimes. This study addresses these gaps through a comprehensive, multi-method dynamical analysis of a representative nonlinear oscillator embodying key FWBK features. Three-dimensional attractor visualizations, return maps, and surrogate data tests demonstrate a transition from quasi-periodic toroidal attractors to fully developed chaos via torus breakdown, confirming that observed complexity originates from deterministic nonlinearity. Poincaré sections reveal multistability and KAM-type structures, where coexisting attractors depend on initial conditions, while increasing noise progressively disrupts coherent dynamics. The OGY control method effectively stabilizes unstable periodic orbits across chaotic regimes with minimal perturbation, and Lyapunov analysis indicates that stochastic forcing attenuates chaos while enhancing dissipation. The Fokker–Planck framework shows that noise reshapes probability landscapes, driving transitions from unimodal to bimodal distributions. Comparative analysis of SINDy, JMAP and VBA highlights trade-offs in interpretability, computational efficiency, and uncertainty quantification, while an integrated Bayesian–PCE–Sobol approach quantifies parametric uncertainty and reveals time-dependent sensitivity variations. Additionally, the overlapping of soliton solutions extracted via the enhanced modified Sardar sub-equation method reveals structural relationships among soliton families and their stability under interaction. Soliton branches that maintain high overlap under noise correspond to stable regimes, while those losing coherence indicate the onset of chaos. Furthermore, while the reduced dynamics in η-space are independent of β, the fractional order controls spatial compression and temporal scaling in physical coordinates, directly influencing observable wave localization. These results imply that fractional effects can modify chaos transitions, support controllability through OGY, and influence noise–instability interactions depending on β. This framework provides a robust, transferable methodology for analyzing and controlling nonlinear oscillatory systems under deterministic and stochastic conditions, with direct applications to FWBK-based models in coastal engineering, fiber optics, and quantum interference systems. Full article
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23 pages, 465 KB  
Article
Analytical Lindblad Dynamics of Field-Controlled Entanglement and State Fidelity in the Hydrogen Electron-Proton Spins: Interplay of Hyperfine Coupling, Zeeman Effects, and Pure Dephasing
by Kamal Berrada and Smail Bougouffa
Axioms 2026, 15(6), 431; https://doi.org/10.3390/axioms15060431 - 10 Jun 2026
Viewed by 247
Abstract
In this paper, we investigate the dynamics of quantum correlations in the ground-state hyperfine manifold of the hydrogen atom subjected to a static external magnetic field and local pure dephasing. The electron–proton spin pair is modeled as a bipartite two-qubit system evolving under [...] Read more.
In this paper, we investigate the dynamics of quantum correlations in the ground-state hyperfine manifold of the hydrogen atom subjected to a static external magnetic field and local pure dephasing. The electron–proton spin pair is modeled as a bipartite two-qubit system evolving under the combined effects of hyperfine coupling, Zeeman splitting, and a Lindblad master equation that describes Markovian dissipative processes. Employing exact analytical solutions for the time-dependent density matrix elements (derived in the Markovian open-system framework), we quantify entanglement persistence via concurrence and state stability via Uhlmann fidelity with respect to the initial preparation. For an initial Werner state, numerical results reveal that the external magnetic field substantially modifies the system dynamics: Both concurrence and fidelity exhibit pronounced dependence on the Zeeman parameter, producing field-controlled oscillations, delayed entanglement sudden death, and altered decoherence rates. This behavior originates from Zeeman-induced lifting of hyperfine degeneracies, symmetry breaking of the isotropic Werner state, and redistribution of populations and coherences. Unlike previous studies that treat hyperfine interactions, Zeeman splitting, or decoherence in isolation, the present work provides a unified analytical treatment that simultaneously incorporates all three mechanisms. The findings underscore the competition between coherent hyperfine coupling and environmental noise and open new pathways for precision spectroscopy and robust quantum information protocols based on atomic spin degrees of freedom. Full article
(This article belongs to the Section Mathematical Physics)
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28 pages, 2857 KB  
Article
Entropy Production from Spin–Vibrational Coupling in Endohedral-Fullerene Qubits Encapsulated in Suspended Carbon Nanotubes
by Cristian Staii
Entropy 2026, 28(6), 646; https://doi.org/10.3390/e28060646 - 8 Jun 2026
Viewed by 355
Abstract
Hybrid carbon nanotube–fullerene architectures provide a controllable setting in which to study irreversibility and information flow in strongly structured quantum environments. We analyze entropy generation in a platform where paramagnetic endohedral fullerenes (PEFs), such as N@C60 and P@C60, are encapsulated [...] Read more.
Hybrid carbon nanotube–fullerene architectures provide a controllable setting in which to study irreversibility and information flow in strongly structured quantum environments. We analyze entropy generation in a platform where paramagnetic endohedral fullerenes (PEFs), such as N@C60 and P@C60, are encapsulated inside a suspended carbon nanotube (CNT) resonator, such that selected multi-level PEF spin states define an effective qubit coupled to quantized CNT flexural modes. Motivated by prior work on fullerene-filled CNTs, on spin–phonon manipulation in suspended nanotubes, and on exact phase-space propagators for damped driven oscillators, we formulate a hybrid open-system description that combines a driven quantum Brownian description of the CNT resonator with an effective Jaynes–Cummings type spin–vibrational interaction. The resonator dynamics are represented in phase space through the Wigner function, whose time evolution can be written analytically in terms of the initial Wigner distribution and a Gaussian propagator. This representation makes it possible to separate drive-induced phase space displacement, diffusion, and damping, and to connect these features directly to entropy flow. The coupled spin–mechanical dynamics are then embedded in a Lindblad quantum master equation that includes mechanical damping, spin relaxation, pure dephasing, and thermally activated excitation channels. Within this framework we derive the entropy balance equation—identifying entropy flux and non-negative entropy production—and examine how hybridization between the molecular spin and the nanotube vibration redistributes irreversibility between coherent exchange and dissipative channels. We show that spin–phonon coupling enhanced by a magnetic field gradient, resonant driving, and moderate thermal occupation can produce identifiable crossovers between entropy–production regimes dominated by the oscillator and those dominated by the spin. The resulting framework provides a quantitative basis for using CNT–PEF hybrids as nanoscale platforms for studying nonequilibrium quantum thermodynamics, decoherence, and information loss in structured vibrational environments. Full article
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