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.

Abstract: NELIPS acronym standing for Nano-Enhanced Laser Induced Plasmas Spectroscopy. Within this framework, the temporal variation of the enhanced emission averaged over different emission wavelengths was measured within delay time from 1 to 7 ms at fixed laser irradiance and gate time of 1ms. Different nanomaterials were employed including silver, zinc, titanium and iron. Both of bulk and pure-nanomaterial plasmas were ignited under similar conditions by Nd-YAG laser radiation at 1064 nm. However, the pure nano-based plasma emission spectral line intensities was reveal to decline at a slower pace with time. Meanwhile, the average enhanced emission was found to increase in an exponential manner with time too. This, and a model was suggested based on the first derivative of enhancement with time, which was found precisely predicts this exponential variation in enhanced emission with time.

Abstract: We investigate how collisional interactions between the condensate and the thermal cloud influence the distinct dynamical regimes (Josephson plasma, phase-slip-induced dissipative regime and macroscopic quantum self-trapping) emerging in ultracold atomic Josephson junctions at non-zero subcritical temperatures. Specifically, we discuss how the self-consistent dynamical inclusion of collisional processes facilitating the exchange of particles between the condensate and the thermal cloud impacts both the condensate and the thermal currents, demonstrating that their relative importance depends on the system's dynamical regime. Our study is performed within the full context of the Zaremba-Nikuni-Griffin (ZNG) formalism, which couples a dissipative Gross-Pitaevskii equation for the condensate dynamics to a quantum Boltzmann equation with collisional terms for the thermal cloud. In the Josephson plasma oscillation and vortex-induced dissipative regimes, collisions markedly alter dynamics at intermediate-to-high temperatures, amplifying damping in the condensate imbalance mode and inducing measurable frequency shifts. In the self-trapping regime, collisions destabilize the system even at low temperatures, prompting a transition to Josephson-like dynamics on a temperature-dependent timescale. Our results show the interplay between coherence, dissipation, and thermal effects in a Bose-Einstein condensate at finite temperature, providing a framework for tailoring Josephson junction dynamics in experimentally accessible regimes.

Abstract: Motivated by two of the most unexpected discoveries in recent years - the detection of ArH+ and HeH+ noble gas molecules in the cold, low-pressure regions of the Universe - we investigate [He2H]+ and [Ne2H]+ as potentially detectable species in the interstellar medium, providing new insights into their energetic and spectral properties. These findings are crucial for advancing our understanding of noble gas chemistry in astrophysical environments. To achieve this, we employed a data-driven approach to construct a high-accuracy, machine-learning potential energy surface (ML-PES) using the reproducing kernel Hilbert space (RKHS) method. Training and testing datasets are generated via high-level CCSD(T)/CBS[56] quantum chemistry computations, followed by a rigorous validation protocol to ensure the reliability of the potential. The ML-PES is then used to compute vibrational states within the MCTDH framework, and assign spectral transitions for the most common isotopologues of these species in the interstellar medium. Our results compared with previously recorded values, revealing that both cations exhibit a prominent proton-shuttle motion within the infrred spectral range, making them strong candidates for telescopic observation. This study provides a solid computational foundation, based on rigorous fully quantum treatments, aiming to assist in the identification of these yet unobserved He/Ne hydride cations in astrophysical environments.

Abstract: We theorize a quantum memory based on the dark-state polariton field, formed by the superposition of atomic and photonic states of a travelling probe laser pulse under the application of a standing wave modes of a dominant control laser pulse using a lambda-level scheme Electromagnetically Induced Transparency in a solid medium. We show how an enhancement in the storage time for the pulse is achieved by eliminating pulse broadening due to diffusion. At last, we propose an experiment that can help realise the storage of a probe pulse in the hyperfine levels 3H4 ↔1D2 of Pr3+: Y2SiO5, cryogenically cooled at 4.5 K. We also discuss multiple applications the storage of the quantum states the pulse probe with a prolonged time interval must have.

Abstract: A novel approach was presented in this study where molecular dynamics and Monte Carlo methods were applied to subatomic particles to simulate an atom using pseudo potentials. Pseudo potentials were developed for subatomic particles by conceptualizing them as conventional particles, exhibiting attractive and repulsive forces between them, ensuring the stability of an atom. A stable nucleus was formed at the center with electrons distributed around, resulting in the formation of an atom. Subatomic particle simulations impart a comprehensive perspective and a profound understanding of electron trajectories that correlates with atomic properties such as electron energies and atomic radius. These approaches intricately capture the impact of protons and neutrons motion in the nucleus on electron trajectories. Hydrogen and carbon atoms were considered, and their analyses were reported in this study. Time step for carbon atom simulation was calculated from dimensionless variables and found to be 1.67 attoseconds. The Pilot-wave theory was implemented to simulate the wave nature of subatomic particles in an atom. Electrons motion were guided by the interference pattern produced by the electron and proton aether medium waves. Molecular dynamics simulations on subatomic particles were implemented on an oxygen molecule, giving insights into electronic structures with electron trajectories shared by two atoms.

Abstract: As one of the most accurate instruments in history, the optical clock will be used as the measuring equipment for the next generation of seconds. The demand for miniaturization of optical clock is progressively urgent. In this paper, a multi-channel radio frequency module with a 20% volume of the commercial module is designed and implemented for the transportable 40Ca+ ion optical clock. Based on the double crystal oscillator interlocking technique，1 GHz low-phase noise reference source is developed for direct digital synthesis. By simulation and optimization of the signal link design, a frequency range of the low-phase noise RF signal can reach 0-400 MHz with a 4 μHz resolution. Through two-stage power amplified with different kinds of filters, it can get an output power up to +33 dBm (2 W) at 100 MHz with a 25 dBc/Hz phase noise lower than the commercial module at 1 Hz, and its third harmonic suppression ratio has been reduced by more than 20 dBm at the frequency point of 300 MHz. This multi-channel RF module is used for the power stability and timing control test of 729 nm clock laser, to meet the requirements of the transportable 40Ca+ optical clock. Without this, this module can also be applied to other quantum systems such as quantum absolute gravimeter, quantum gyro and quantum computer.