Abstract: String theory has long pursued a mechanism to compactify its extra dimensions into the observable physical constants of our universe, yet the vast landscape of ~10⁵⁰⁰ possible vacua remains unresolved. Our 4G Model Solution: The 4G Model introduces four interaction-dependent scalar gravitational constants (GN, Ge, Gn, Gw) as the practical bridge, deriving a fundamental 33 pm interaction length—the geometric mean of nuclear and electromagnetic gravity. This scale constrains atomic structure and nuclear radii via the empirical A¹/³ scaling law. Validation: The 4G Model’s fundamental scaling law (A¹/³ × 33 pm) predicts Carbon’s covalent radius at 75.6 pm-matching the experimental 75 pm value to under 1% error without the proposed common correction term. This precise agreement without corrections suggests that the geometric mean of nuclear and electromagnetic gravity [√(Gn*Ge)] may play a key role in atomic structure. Broader Deviations Contextualized: Secondary deviations in other groups stem from Z-dependent quantum screening of Ge and Gn, not flaws in the underlying scale- paralleling Bohr model successes for hydrogen before Sommerfeld’s fine-structure refinements addressed relativistic effects. Theoretical Confirmation: This selective precision affirms 4G’s unification: atomic radii emerge directly from string-like compactification geometry, with screening as tunable perturbations. Carbon’s validation anchors the model as a working hypothesis, indicating that gravitational constants could play a significant role in constraining chemistry at the 33 pm scale. Extension: Finally, by applying the proton’s charge‑mass “dual discreteness formalism,” we propose that atoms can be interpreted as quantum gravitational compact objects within this framework. These are structured into a hierarchy of 7 fundamental shells, dictated by the stability condition , n=1,2,3.., Z/Root(A) . Light magic numbers emerge from the integer values of Z/Root(A_stable) , while heavy magic numbers correspond to the half-integer form, [Z/Root(A_stable)+0.5].

Abstract: Electron collision broadening parameters calculations were performed for 33 singly ionized yttrium spectral lines, 27 with special relevance in astrophysical applications (can be found in the Atmospheres of FGK Stars). Calculations were made in the semi-empirical Griem approach using the Gaunt factors proposed by Van Regemorter and those proposed by Douglas H. Sampson. Furthermore, to test our calculations, the electron collision broadening of 4 well isolated spectral lines of Y II was experimentally measured in laser- induced breakdown experiments using a Q-switched Nd:YAG laser focused on Pb-Y alloy samples.

Abstract: The Theory of Inventive Problem Solving (TRIZ) has long been a cornerstone for systematic innovation in engineering domains, including chemical and materials science. This paper proposes a novel framework that integrates TRIZ principles with large language models (LLMs) to emulate researcher-like reasoning in atomistic materials science. By structuring LLM prompts around TRIZ tools—such as patterns of evolution, contradiction matrices, and inventive principles—we enable models to identify problems, frame contradictions, and generate inventive solutions for challenges like data scarcity, poor interpretability, and unphysical predictions in quantum-chemical simulations and machine learning (ML) models. Drawing on recent artificial intelligence-TRIZ hybrids, like AutoTRIZ and TRIZ-GPT (generative pre-trained transformer), we demonstrate applications in molecular design, such as resolving contradictions in shape-memory polymers. This approach not only amplifies current trends in physics-informed ML and generative design but also democratizes advanced problem-solving, accelerating discoveries toward ideality

Abstract: Resonant transfer and excitation (RTE) is a correlated two-electron process mediated by the two-center electron-electron interaction: A projectile electron is excited while a target electron is captured, forming doubly excited states. These decay via X-ray (RTEX) or Auger (RTEA) emission. For fast enough collisions with light targets, RTE becomes analogous to dielectronic capture (DC)—a key plasma process—and is described by the impulse approximation (IA). Early (1983–1992) RTEX and the more stringent, state-selective RTEA measurements at accelerator facilities provided indirectly, essential DC cross section information before direct electron-ion DC measurements became available. The 1992 review [1], focusing on zero-degree Auger projectile spectroscopy (ZAPS) of state-selective KLL D states, validated the IA for low-Z_p ions (Z_p ≤ 9). However, a puzzling systematic discrepancy was revealed: IA cross sections were consistently larger than experiment, with the disagreement increasing as projectile atomic number Z_p decreased. This review updates RTEA progress since 1992: Refinements to IA calculations include the use of more accurate Auger rates, considerations of Auger anisotropic emission, novel target binding corrections and even an exact IA formulation. Experimental ZAPS improvements feature a hemispherical spectrograph and a proven in situ more accurate standardized absolute cross section calibration using binary encounter electrons. A methodical analysis demonstrates impressive agreement across all measurements spanning both pre- and post-1992 eras including measurements presented here for the first time, eliminating systematic discrepancies. IA validity is confirmed down to boron ions, with He⁺ ions as the sole clear exception together with some borderline Li-like ion cases. Recently, a rigorous ion-atom collision treatment has also emerged: Nonperturbative close-coupling calculations of transfer excitation of He-like ions in collisions with He confirms RTE dominance via two-center electron-electron interactions at large impact parameters, while providing unexpected insights into many-body collision dynamics at the lowest collision energies.

Abstract: We show time reversal asymmetry in quantum mechanics by isolating a single, solitary hydrogen atom in a black body, deriving from it the diagonalized Hamiltonian matrix in continuous time, and using it to visualize the irreversibility of the emission and absorption of radiation. Graphic evidence in support of the model is obtained from experiments performed with the simplest quantum system, an electron cyclotron. The experimental evidence is used to obtain equations of motion to describe time asymmetry with respect to the energy-time conjugate variables in linear time which complement the time symmetric equations of motion in position-momentum coordinates given with respect to cyclical time. Theoretical arguments by Feynman and Einstein are shown to support time reversal asymmetry.

Abstract: N-dimensional simplices, apart of their highly symmetric properties, exhibit interesting properties, both in the structure of the coordinates of their vertices and in the uniform distances between pairs of them. Relationships of simplices with the vertices of dimensional hypercubes are also of interest. Discussing these facts in depth as an introduction, the present study examines the implications of the coordinate structure of simplices for the Theoretical and Quantum Mechanical formalism, applied to swarms of particles located at the vertices of a simplex. Also, the properties of the topological matrices that represent such a distance-conformation will be studied. Some interesting results arise from this analysis. Among others, a paradox about the existence of swarms of particles with dimensional simplex-vertex distance structure and the possibility of overcoming it, allowing the description of an dimensional description of the particles’ location. A brief discussion on the time-dependence of simplex coordinates is also provided.

Abstract: For nearly a century screened Coulomb potentials have been of recognized importance in diverse areas of physics and chemistry. A key feature of interest in these potentials is the phenomenon of critical screening. This paper has three main purposes: To present an extensive, open-access, high accuracy (60 digit) benchmark reference data set of critical screening parameters, with validation; to confirm excellent past work in the field (to 30 digits), and to correct an historical oversight in its literature; and to present the essentials of our new approach, the “Phase Method” (PM), for computing them. Using the PM we calculate critical screening parameters, accurate to 60 decimal digits, for the Yukawa/Debye, Hulthén, Pseudo-Hulthén, and Exponential Cosine Screened Coulomb (ECSC)) potentials. The practical feasibility of such calculations on inexpensive hardware opens up new possibilities in research and education. We highlight an apparently overlooked 1989 paper of Demiralp on critical screening parameters of the Yukawa potential, which accurately calculated them to 30 decimal digits. Our main results are computations of the critical screening parameters µ_c= 1/D_c for screening lengths D ≤ 1000 au and angular momenta l = 0 . . . 20. The claimed accuracy of our results is supported by several independent lines of evidence: comparison with the most accurate (30 digit) values available in the print literature for the Yukawa, Hulthén, and ECSC potentials; comparison to 60 decimal digits accuracy with exactly known eigenvalues and critical binding parameters of the Pseudo-Hulthén potential; consistency tests between computed critical parameters, for various l-values for the Pseudo-Hulthén Potential, and known exact relations between eigenvalues; and application of a novel consistency test between results with different potential parameters, that exploits an exact scaling symmetry of this entire class of potentials. Similar calculations were done for ECSC and Yukawa potentials for screening lengths up to D ≤ 10⁵ and l ≤ 12, to 30 digit accuracy, which show interesting (and to our knowledge not previously reported) periodic structure in D_c(n, l) for the ECSC potential that is not observed for the Yukawa potential. The asymptotic scaling behavior for the Yukawa and Hulthén potentials is explained quantitatively by simple semiclassical calculations.

Abstract: We propose a novel theoretical framework for describing photon--electron interactions and electron collision processes in a unified manner within quantum electrodynamics. Specifically, we develop a method to construct the Dirac operator in curved spacetime using only matrix representations rooted in the basis structure of four-dimensional gamma matrix algebra, without introducing vierbeins (tetrads) or independent spin connections. We realize 16 gamma matrices with two indices as $256\times256$ matrices and embed the spacetime metric directly into the matrix elements. This reduces geometric operations such as covariantization, connection-like operations, and basis transformations to matrix products and trace calculations, yielding a unified and transparent computational scheme. The spacetime dimension remains four, and the number ``16'' represents the number of basis elements of four-dimensional gamma matrix algebra ($2^{4}=16$). Based on the extended QED Lagrangian, vertex rules, propagators, spin sums, and traces can be handled uniformly, making it suitable for automation. As validation of this method, we analyzed four fundamental scattering processes in atomic and particle physics: (i) Compton scattering (photon--electron scattering), (ii) muon pair production ($e^+e^-\to\mu^+\mu^-$), (iii) M{\o}ller scattering (electron--electron collision), and (iv) Bhabha scattering (electron--positron collision). In the flat spacetime limit, we confirmed exact reproduction of standard quantum electrodynamics (QED) results including the Klein--Nishina formula. Furthermore, trial calculations using a metric with off-diagonal components show systematic deviations from flat results near scattering angle $\theta\approx90^{\circ}$, suggesting that metric-induced angular dependence could in principle serve as an observable signature. The matrix representation developed in this work enables unified pipeline execution of theoretical calculations for photon interactions and charged particle collision processes, with expected applications to precision calculations in atomic and particle physics.

Abstract: Reliable estimation of kinetic parameters in molecular dynamics (MD) requires distinguishing physical phenomena from numerical artifacts. Standard MD workflows often mask integration errors through empirical damping, potentially obscuring rare configurational transitions. We introduce a calibration framework employing intentionally conservative numerical parameters—including reduced timesteps (0.10 fs) and attenuated intermolecular forces—to establish a numerical fidelity baseline. This approach isolates integration artifacts from force-field complexities, providing a reference against which production MD methods can be benchmarked. By demonstrating stable integration under maximally challenging conditions, we provide a methodology for validating the numerical foundations of kinetic inference in drug discovery applications.

Abstract: This paper aims to provide a thorough critical analysis of two foundational concepts in modern physics — the Landé g-factor and the electron spin quantum number 1/2. Through meticulous historical examination and logical analysis, this paper argues that these concepts are essentially mathematical fitting parameters introduced to bridge the gap between the old quantum theory and experimental data, lacking a solid foundation in physical mechanism. The core contradiction lies in the subsequent development of wave mechanics, which concluded that "the orbital angular momentum of the hydrogen atom ground state is zero," a conclusion that fundamentally conflicts with observational facts such as the Stern-Gerlach experiment, forcing the spin concept to assume a "remedial" role it never needed to bear. As a solution, this paper presents a new framework based on the "Great Tao Model" and the "Unified Theory of Atomic and Molecular Structure." This framework firmly returns to the realism of classical physics, affirms the orbital motion of electrons around the nucleus and their intrinsic angular momentum, and interprets spin as a real mechanical motion. Crucially, this theory naturally derives the universal magnetic moment-angular momentum relation μ = (e/m) L from the "Existence Field" principle, eliminating the need for any artificial correction factors. Based on this, the paper successfully provides a unified and self-consistent explanation for key phenomena such as the Stern-Gerlach experiment and the normal and anomalous Zeeman effects, thereby achieving a simpler and more fundamental description of physics at the atomic scale.

Abstract: A program package for calculating regularized classical trajectories for Coulomb n−body problem is developed. The Coulomb singularities from the equations of motion are removed by transformations of variables including the time. This effectively conserves the energy of the time-independent systems to a high accuracy for long time propagation. Sample calculations are shown for the cases of 2,3,4, and 5 particle systems giving comparisons with the un-regularized trajectories. The program can be used for general purposes including the classical-trajectory Monte-Carlo simulations for charged-particle collisions in free or laser environments.

Abstract: Revealing the structure of atoms and molecules has always been one of the important research goals in the field of quantum mechanics. The currently well-known atomic and molecular structure theories include Rutherford's planetary model, Bohr Sommerfeld atomic structure model, as well as atomic orbital theory, hybrid orbital theory, and molecular orbital theory. However, although these theories can explain atomic or molecular structures to some extent, they all have their own shortcomings, and there is currently no unified theory of atomic and molecular structures established. Here, we propose the Dynamic Entity Model of Electron Orbits, the Electron Spin Theory, and the Spatial Configuration Theory of Electron Orbits. Based on these new concepts and theories, we rearranged the extranuclear electrons of all elements in the periodic table, and explained the structure of atoms, the physical mechanisms of molecular formation, and the spatial structure of molecules. The theories of atomic and molecular structures based on quantum mechanics are often complex, difficult to understand, and inconsistent, while our new concepts and theories are based on classical physics and have the characteristics of being simple, intuitive, and easy to understand, and can logically and consistently explain the structure of atoms and molecules. Therefore, we have established a unified atomic and molecular structure theory based on the framework of classical physics, which has important scientific significance and application value.

Abstract: Spectral line broadening is a central diagnostic in atomic physics and astrophysics, yet residual linewidths remain even after accounting for conventional mechanisms such as natural, Doppler, collisional, and Stark or Zeeman effects. This study introduces the concept of coherence restructuring work as defined in the First Law of Coherence Thermodynamics, proposing that residual broadening represents the dissipative footprint of non Markovian field engagement. The approach extends thermodynamic formalism to include a memory dependent functional derived from generalized Langevin dynamics, and applies it to atomic spectra. We explain why hydrogen spectra exhibit minimal restructuring, while multi electron atoms and astrophysical systems reveal broadened lines consistent with history dependent coherence demands. Conclusions indicate that residual linewidths encode structural learning processes, reframing quantum collapse as a thermodynamic phenomenon driven by coherence restructuring rather than observer dependent measurement. This interpretation unifies atomic, stellar, and gravitational systems under a single coherence principle, offering a measurable pathway to probe non Markovian dynamics in both laboratory and astrophysical contexts.

Abstract: We present a geometric resolution of the Yang–Mills mass gap problem, one of the seven Clay Millennium Prize problems in mathematics. Within the QRECOIL (Quantum Resonant Emergence through Chaos, Ontology, and Informational Loops) framework, we demonstrate that the mass gap emerges necessarily from three syn- ergistic mechanisms: (i) the discrete eigenvalue spectrum of the Laplace–Beltrami operator on the 3-sphere S3 ∼= SU(2), (ii) von Neumann entropy minimization through Fibonacci quantization governed by the golden ratio φ = (1 + √5)/2, and (iii) topological protection via the second Chern class c2(S3) = 3. We derive the fundamental mass gap formula ∆YM = ΛQCD ×φ ≈ 1.699 GeV, achieving agreement with lattice QCD glueball masses within 0.3% without parameter fitting. Crucially, the golden ratio emerges naturally from Jacobi polynomial recursion on S3 for SU(3) gauge theoryit is mathematical consequence, not empirical input. We estab- lish three independent proofs that ∆YM > 0 is geometrically necessary, addressing the core requirement of the Clay Institute problem. This work demonstrates that confinement and mass generation are geometric inevitabilities arising from the compactification of gauge coupling space onto S3, providing a pathway toward rigorous resolution of the Yang–Mills existence and mass gap problem.

Abstract: We present a time-dependent nonperturbative theory of the reconstruction of attosecond beating by interference of multiphoton transitions (RABBIT) for photoelectron emission from hydrogen atoms in the direction perpendicular to the laser polarization axis. Extending our recent semiclassical strong-field approximation (SFA) model developed for parallel emission [López et al., Phys. Rev. A 110, 013104 (2024)], we derive analytical expressions for the transition amplitudes and demonstrate that the photoelectron probability distribution can be factorized into interhalf- and intrahalfcycle interference contributions, the latter modulating the intercycle pattern responsible for sideband formation. We identify the intrahalfcycle interference between trajectories born within the same half cycle as the mechanism governing attosecond phase delays in the perpendicular geometry. Our results reveal the suppression of even-order sidebands due to destructive interhalfcycle interference, leading to a characteristic spacing between adjacent peaks that doubles the standard spacing observed along the polarization axis. Comparisons with numerical calculations of the SFA and the ab initio solution of the time-dependent Schrödinger equation confirm the accuracy of the semiclassical description. This work provides a unified framework for understanding quantum interferences in attosecond chronoscopy, bridging the cases of parallel and perpendicular electron emission in RABBIT-like protocols.

Abstract: In this study, the spectroscopic and aromaticity properties of newly synthesized methylene bridged [6], [8] and [10] rings of p-styrene (MCPP) were investigated. The photophysical properties of MCPP with n=6, 8 and 10 are calculated and analyzed by time-varying density functional theory (TD-DFT). The main characteristics of Raman spectra are revealed by vibration analysis. The results show that the contribution of π orbital to electron excitation is the main cause of antiaromaticity. By means of induced current density anisotropy (AICD), isochemical shield surface (ICSS) and magnetic induction galvanometer (GIMIC), the responses of these molecules to external magnetic fields, especially the ring current induction and magnetic shield effects, were investigated. The results show that these MCPP systems exhibit anti-aromaticity, which is mainly driven by the delocalization of strong π electrons. This study deepens the understanding of the structure and electronic properties of MCPP, and provides a reference for practical application in material design in the future.

Abstract: Collective superradiant decay of a tightly packed inverted quantum emitter ensemble is among the most intensely studied phenomena in quantum optics. Since the seminal work of Dicke more than half a century ago, a plethora of theoretical calculations in quantum many-body physics have followed. Widespread experimental efforts range from the microwave to the X-ray regime. Nevertheless, accurate calculations of the time dynamics of the superradiant emission pulse still remain a challenging task needing approximate methods for large ensembles. Here, we benchmark the cumulant expansion method for describing collective superradiant decay against a new, recently found exact solution. Applying two variants of the cumulant expansion exhibits reliable convergence of time and magnitude of the maximum emission power with increasing truncation order. The longterm population evolution is only correctly captured for low emitter numbers, where an individual spin-based cumulant expansion proves more reliable than the collective spin-based variant. Surprisingly, odd orders show even qualitatively nonphysical behavior. At sufficiently high spin numbers, both chosen cumulant methods agree, but still fail to reliably converge to the numerically exact result. Generally, at a longer time scale, the expansions substantially overestimate the remaining population. While numerically fast and efficient, cumulant expansion methods need to be treated with sufficient caution when applied for long-time evolution or reliably finding steady states.

Abstract: We present a comprehensive information-theoretic evaluation of three widely-used rigid water models (TIP3P, SPC, and SPC/ε) through systematic analysis of water clusters of varying sizes (1M, 3M, 5M, 7M, 9M, and 11M molecules). Five fundamental descriptors—Shannon entropy, Fisher information, disequilibrium, LMC complexity, and Fisher-Shannon complexity—were calculated in both position and momentum spaces to quantify electronic delocalizability, localization, uniformity, and structural sophistication. Molecular dynamics simulations validated the force fields against experimental bulk properties (density, dielectric constant, self-diffusion coefficient), while statistical analysis using Shapiro-Wilk normality tests and Student’s t-tests ensured robust discrimination between models. Our results reveal distinct scaling behaviors that correlate with experimental accuracy: SPC/ε demonstrates superior electronic structure representation with optimal entropy-information balance and enhanced complexity measures, while TIP3P shows excessive localization and reduced complexity that worsen with increasing cluster size. The methodology establishes information theory as a powerful framework for force field evaluation, providing quantitative insights into scalability and transferability from clusters to bulk water systems.

Abstract: In Classical Mechanics, time is reversible, i.e. implies no particular choice: only the observer knows in which direction it flows. The present Comment re-examines whether this remains true in Quantum Mechanics. In the context of Atomic Physics, it is concluded that the existence of an arrow of time depends on the manner in which the radiation field is introduced, which must be non-perturbative.

Abstract: A combined experimental and theoretical study is carried out on the single-electron capture process in He+-He collisions at energies ranging from 0.5 to 5 keV/u. Using cold target recoil ion momentum spectroscopy, we obtain state-selective cross sections and angular differential cross sections. Within the entire studied energy range, the dominant channel is the electron captured into the ground-state, and the relative contribution of the dominant channel shows a decreasing trend with increasing energy. The angular differential cross sections of ground-state capture exhibit obvious oscillatory structures. To understand the oscillatory structures of the differential cross sections, we also performed theoretical calculations using the two-center atomic orbital close-coupling method, which well reproduced the oscillatory structures. The results indicate that these structures are strongly correlated to the oscillatory structures of the impact parameter dependence of electron probability.