A bstract We describe in detail the implementation of the relativistic three-neutron finite-volume quantization condition derived in ref. [1]. In particular, we show how the complications due to Wigner rotations acting on spins are included, and present concrete formulas for the case when the angular momenta within pairs is restricted to be less than 2. We describe the symmetries of the matrices appearing in the quantization condition, and decompose solutions into irreducible representations of the appropriate doubled finite-volume symmetry groups. We present an implementation of the three-particle K matrix, keeping the two lowest-order terms in the threshold expansion. We provide numerical predictions for the finite-volume spectrum for a setup with nearly physical parameters, including two-particle interactions that are based on experimental results. This exploratory study shows the how lattice QCD calculations of the three-neutron spectrum with sufficient precision can provide detailed information on both two- and three-particle interactions.

This article provides a rigorous study of Airy functions, emphasizing their constructionby power series, their relation with Bessel functions, and their canonical integral representation. Wehighlight their asymptotic properties and structural role in mathematical physics. To illustrate theirapplicability, we develop three analytical models: the Euler–Bernoulli beam under self-weight, thequantum bouncer with a linear gravitational potential, and the particle in a uniform electric field.In each case, the quantization conditions and physical scales naturally emerge from the zeros ofthe Airy function. These results confirm the central role of Airy functions in bridging differentialequations, special functions, and applied physics.

ABSTRACT We propose a manifestly duality‐invariant, Lorentz‐invariant, and local action to describe quantum electrodynamics in the presence of magnetic monopoles that derives from Sen's formalism. By employing field strengths as the dynamical variables, rather than potentials, this formalism resolves longstanding ambiguities in prior frameworks. Our analysis finds consistent outcomes at both tree and loop levels using the established principles of quantum field theory, obviating the need for external assumptions or amendments. We clarify the mechanisms of charge renormalization and demonstrate the renormalization group invariance of the charge quantization condition. Our approach can be useful for phenomenological studies and in quantum field theories with strong–weak dualities.

A bstract We extend the relativistic field theoretic finite-volume formalism to Nππ scattering states at maximal isospin, I = 5 / 2. As in previous work using the relativistic field theory approach, we work to all orders in a generic low-energy effective theory, and determine the quantization condition that relates finite-volume energies to intermediate K matrices, and the integral equations connecting the latter to the physical scattering amplitudes. We discuss the parametrization of the K matrices, and explain in detail the new features that arise in implementing the quantization condition due to the spin of the nucleon in combination with the use of non-degenerate particles. As a concrete example, we provide a sample numerical application including the ∆ resonance in the Nπ subchannel. The extension to the I = 3 / 2 and 1 / 2 channels is more involved, due to mixing with Nπ states, and we do not provide a complete formalism for these cases. We explain why Nπ states cannot be included by treating the nucleon as a pole in p -wave Nπ scattering, an approach that has been successful in studying DD * scattering using the three-particle DDπ formalism. We additionally provide results for all isospins under the assumption of no two-to-three mixing, thereby laying the groundwork for a follow-up paper in which all Nππ → Nπ systems are fully treated. Finally, we study the singularities in Nππ amplitudes arising from Nπππ intermediate states, and find that our subthreshold cutoff functions must be modified to avoid such singularities.

We employ the density-dependent cluster model to calculate alpha-decay half-lives of recently synthesized superheavy nuclei (SHN) with Z=104–118. A microscopic alpha–nucleus potential is derived via the double-folding method using a realistic nucleon–nucleon interaction. Within the Wentzel–Kramers–Brillouin approximation, supplemented by the Bohr–Sommerfeld quantization condition, we extract both the alpha-particle assault frequency and barrier-penetration probability for spherical and deformed daughter configurations. Our predictions for five isotopes of the superheavy element Z=123 are benchmarked against several established models, demonstrating excellent agreement. We also explore the competition between alpha-decay and spontaneous fission, and propose likely decay chains for the as-yet unobserved nuclei {}^{302text {--}307}123. Finally, cluster-decay channels of {}^{300,303,306,307}123 are studied using the double-folding potential alongside the Universal curve (UNIV), the Universal Decay Law (UDL), the Unified Decay Formula (UDF), and Horoi’s approach. Notably, the UDL framework predicts positive branching ratios log _{10}b_c for heavy-cluster emission (e.g. ^{90}textrm{Sr}, ^{96}textrm{Zr}, ^{102}textrm{Mo}), indicating that such clusters may rival—or even dominate—alpha-decay in these SHN.

Spiral Compactification with torsion-monodromy locking

A global potential constrained by the Bohr-Sommerfeld quantization condition for $\alpha$-decay half-lives of even-even nuclei

The periodic solution of the Friedmann equation in conformal time implies that only cosmological perturbations exhibiting corresponding symmetries are physically permissible, leading to a discrete spectrum of allowed wave vectors. Furthermore, in a spatially closed universe, these wave vectors are independently constrained to be integers. Matching these two distinct quantization conditions provides a novel theoretical constraint on the possible values of spatial curvature. In this work, we numerically solve the cosmological perturbation equations, incorporating radiation anisotropy and higher-order Boltzmann terms, to calculate these discrete wave vectors with improved precision. Subsequently, we generate cosmic microwave background power spectra for different characteristic spacings of these quantized wave vectors. Finally, we apply the constraint to Planck 2018 observational data to determine the cosmological parameters. This analysis yields a discrete set of allowed values for the spatial curvature, Ω K , 0 , including [ − 0.076 , − 0.039 , − 0.024 , − 0.016 , − 0.012 , … ] .

This paper investigates the performance of affine frequency division multiplexing (AFDM) under finite-resolution analog-to-digital converters (ADCs) and practical hardware impairments, as well as realistic channel estimation. The additive quantization noise model (AQNM) is adopted to characterize ADC quantization errors, while the generalized complex exponential basis expansion model (GCE-BEM) is employed to model time-varying channels. Based on these models, we derive a closed-form expression for the normalized mean-square error (NMSE) of the channel estimation in the presence of ADC quantization and hardware impairments. Furthermore, we theoretically analyze the impact of finite-precision quantization and non-ideal hardware conditions on the bit error rate (BER), revealing the intrinsic relationship among BER, quantization resolution, and hardware impairments, thereby offering useful guidelines for practical system design. Simulation results validate the derived NMSE and BER analyses and demonstrate the sensitivity of AFDM performance to ADC resolution and hardware impairments. Additionally, our results confirm a resolution saturation region of AFDM around 6 bits, at which point thermal noise dominates and quantization can be disregarded.

We develop a new method for writing simple exact equations characterizing gravity solutions among which are black holes and in particular quasinormal modes. More precisely, we derive the full system of functional and thermodynamic Bethe ansatz nonlinear integral equations of quantum integrability. In particular, we prove that the quasinormal modes verify different equivalent exact quantization conditions and identify them with Bethe roots. We numerically solve the integral equation and compare the results with other methods. Eventually, we can definitely certify its simplicity, accuracy, and effectiveness. Furthermore, this method connects different unexpected fields and paves the way for innovative ways of investigations in gravity and gauge theories.

Classical and quantum atomic models have succeeded in describing matter at different scales, yet the origin of mass, the neutron–proton mass difference, and the stability of nuclei remain unresolved. We propose the Lattice–Wave Atomic Model (LWAM), in which the nucleus is treated as a three-dimensional oscillatory lattice and nucleons and electrons emerge as standing-wave resonances. Starting from a lattice-wave Lagrangian, we derive quantization conditions for nucleon shells, a resonance-based formula for mass, and an exponential law for decay probabilities. As a test case, we apply LWAM to calculate the binding energy of Helium-4, achieving consistency with empirical values within an order of magnitude. This work suggests that LWAM can serve as a bridge between quantum chromodynamics (QCD) and classical wave mechanics, providing a geometric–resonance interpretation of atomic structure.

Abstract In lattice gauge theory with compact gauge field variables, an introduction of the gauge field topology requires the assumption that lattice field configurations are sufficiently smooth. This assumption is referred to as the admissibility condition. However, the admissibility condition always ensures the Bianchi identity, and thus prohibits the existence of magnetic objects such as the ’t Hooft line. Recently, in 2D compact scalar field theory, Ref. 1) proposed a method to define magnetic objects without violating the admissibility condition by introducing holes into the lattice. In this paper, we extend this “excision method” to 4D Maxwell theory and propose a new definition of the ’t Hooft line on the lattice. Using this definition, we first demonstrate a lattice counterpart of the Witten effect which endows the ’t Hooft line with electric charge and make it a dyon. Furthermore, we show that by interpreting the ’t Hooft line as a boundary of the lattice system, the statistics of the dyon can be directly read off. We also explain how the dyonic operator which satisfies the Dirac quantization condition becomes a genuine loop operator even at finite lattice spacings.

Abstract The Wentzel-Kramers-Brillouin semiclassical method is formulated for quasiparticles with quartic-in-momentum dispersion which presents the simplest case of a soft energy-momentum dispersion. It is shown that matching wave functions in the classically
forbidden and allowed regions requires the consideration of higher-order Airy-type functions. The asymptotics of these functions are
found by using the method of steepest descents and contain additional exponentially suppressed contributions known as hyperasymptotics. These hyperasymptotics are crucially important for the correct matching of wave functions in vicinity of turning points for higher-order differential equations. A quantization condition for bound state energies is obtained, which generalizes the standard
Bohr-Sommerfeld quantization condition for particles with quadratic energy-momentum dispersion and contains non-perturbative in $\hbar$ correction. This non-perturbative correction, usually associated with tunneling effects or the presence of complex turning points, occurs even for the harmonic potential with quartic dispersion where complex turning points and tunneling are absent. The quantization condition is used to find bound state energies in the case of quadratic and quartic potentials.

Recent experiments in rhombohedrally stacked multilayer graphene heterostructures have reported signatures of chiral superconductivity, emerging from a spin- and valley-polarized normal state with broken time-reversal symmetry and an associated anomalous Hall effect. These findings bring into focus the role of the electronic Bloch wave function and the quantum geometric tensor in determining the superconducting pairing channel. In this work, we examine superconducting instabilities of a model of $N$-layer rhombohedral graphene that possesses an enhanced Berry curvature distribution on an extended ring in momentum space, that we dub the ``Berry ring of fire,'' in the presence of an isotropic attractive interaction with a parametrically controlled spatial range. We determine that local interactions favor a $N$-fold winding in the order parameter phase for odd-$N$ layered systems, with even-$N$ layers requiring a spatially extended attraction range to achieve pairing. For generic interaction lengths, we discover a family of chiral superconductors and, remarkably, momentum-space vortices nucleated on the Berry ring of fire. The existence of these vortices can be traced to a momentum-space flux quantization condition involving the Berry curvature, with the phase winding dictated by a combination of the Berry flux and a ``statistical flux'' to enforce Fermi-Dirac statistics. Such an order-parameter structure allows for the possibility of in situ tuning between various chiral superconducting phases through changes in the electron density or the displacement field. We discuss ways in which these predictions can be experimentally tested and potentially exploited in future devices.

Abstract In the present work, based on the Wentzel-Kramers-Brillouin (WKB) approximation and Bohr-Sommerfeld quantization condition, we extend a phenomenological modified harmonic oscillator potential model proposed by Bayrak [J. Phys. G 47: 025102, 2020] to systematically investigate the favored proton radioactivity by considering the spectroscopic factors Sp from the relativistic mean-field (RMF) theory and the BCS method. Calculations show good agreement with experimental data , within a factor of 2.7. Furthermore, employing this model, we predict the proton radioactivity half-lives of potential candidates that are energetically allowed or observed but not yet quantified in the latest atomic mass excess NUBASE2020. For comparison, the one-parameter model (OPM) [Commun. Theor. Phys. 74: 115302, 2022] and the universal decay law (UDLP) [Phys. Rev. C 85: 011303, 2012] are also employed. All the corresponding predictions are consistent with each other. In addition, the reliability of our predictions are further confirmed by comparing the simple formula proposed by Delion et al. [Phys. Rev.Lett. 96: 072501, 2006] and the new Geiger-Nuttall law put forward by Chen et al. [Eur. Phys.J. A 55: 214, 2019].

Abstract Excitons, i.e., the bound states of an electron and a positively charged hole, are the solid-state analog of the hydrogen atom. As such, they exhibit a Rydberg series, which in cuprous oxide has been observed up to high principal quantum numbers by Kazimierczuk et al. (Nature 514:343–347, 2014. https://doi.org/10.1038/nature13832 ). In this energy regime, the quantum mechanical properties of the system can be understood in terms of classical orbits by the application of semiclassical techniques. In fact, the first theoretical explanation of the spectrum of the hydrogen atom within Bohr’s atomic model was a semiclassical one using classical orbits and a quantization condition for the angular momentum. Contrary to the hydrogen atom, the degeneracy of states with the same principal quantum number n is lifted in exciton spectra. This is similar to the situation in alkali atoms, where these splittings are caused by the interaction of the excited electron with the ionic core. For excitons in cuprous oxide, these splittings occur due to the influence of the complex band structure of the crystal. Using an adiabatic approach and analytically derived energy surfaces, we develop a semiclassical spherical model and determine, via semiclassical torus quantization, the quantum defects of various angular momentum states.

In this paper, we analyze the asymptotic behaviour of the poles of certain rational solutions of the fifth Painlevé equation. These solutions are constructed by relating the corresponding tau function to a Hankel determinant of a certain sequence of moments. This approach was also used by one of the authors and collaborators in the study of the rational solutions of the second Painlevé equation. More specifically, we study the roots of the corresponding polynomial tau function, whose location corresponds to the poles of the associated rational solution. We show that, upon suitable rescaling, the roots asymptotically fill a region bounded by analytic arcs when the degree of the polynomial tau function tends to infinity and the other parameters are kept fixed. Moreover, we provide an approximate location of these roots within the region in terms of suitable quantization conditions.

Abstract We introduce gravitational length stretching (GLS) as a novel quantum-gravitational phenomenon that distorts the spatial probability distribution of quantum particles in curved spacetime. Through quantum field theory in curved spacetime (QFT-CS), we demonstrate that GLS originates from the amplitude modulation function B k ( t , x → ) {B}_{k}\left(t,\overrightarrow{x}) in WKB solutions, governed by the covariant continuity equation ∇ μ ( B k 2 k μ ) = 0 {\nabla }_{\mu }\left({B}_{k}^{2}{k}^{\mu })=0 . This effect causes quantum objects to stretch in regions of stronger curvature, increasing their proper spatial extent by ∼ 20 % \sim 20 \% over millimeter scales for ultracold neutrons (UCNs) in Earth’s gravity. Our derivation of the Schrödinger equation in weak gravitational fields from the Klein–Gordon equation in Cartesian Schwarzschild coordinates reveals curvature-induced corrections absent in semi-classical approaches. Crucially, QFT-CS yields a covariant quantization condition ∫ k μ d x μ = n π \int {k}_{\mu }{\rm{d}}{x}^{\mu }=n\pi , resolving ambiguities in the noncovariant semi-classical formalism. We predict observable energy level shifts ( Δ E n ∕ E n ∼ 1 % \Delta {E}_{n}/{E}_{n}\hspace{0.33em} \sim \hspace{0.33em}1 \% ) and probability density gradients ( ∂ z B k 2 ≈ 202 m − 1 {\partial }_{z}{B}_{k}^{2}\approx 202\hspace{0.33em}{{\rm{m}}}^{-1} ) for UCN interferometry, providing a pathway to test GLS in terrestrial laboratories. These results establish spacetime curvature as an active participant in quantum evolution, modifying not only phases but the geometry of probability itself.

A bstract Nuclear matter with a strong magnetic field is prevalent inside neutron stars and heavy-ion collisions. In a sufficiently large magnetic field, the ground state is either a chiral soliton lattice (CSL), an array of solitons of the neutral pion field, or a domain-wall Skyrmion phase in which Skyrmions emerge inside the chiral solitons. In the region of large chemical potential and a magnetic field lower than its critical value for CSL, a Skyrmion crystal is expected to take up the ground state based on the chiral perturbation theory at the next leading order. We determine the phase boundary between such a Skyrmion crystal and the QCD vacuum. We examine the previous conjecture that a Skyrmion in magnetic field could be in a form of a neutral pion domain wall bounded by a superconducting ring of charged pions with the radius determined by the quantization condition of the penetrating magnetic flux. We also validate that a Skyrmion would shrink to null without the Skyrme term, although Derrick’s scaling law is modified by a background magnetic field, and the stability at the leading order is not ruled out in theory.

In this study, we analyze the bound-state energy spectrum of quark-antiquark systems using the semiclassical WKB approximation. We consider the Cornell potential, which combines a linear confinement term with a Coulombic interaction, and perform a Taylor series expansion around an appropriately chosen point [Formula: see text] to simplify the potential near the classical turning points. This expansion enables an analytic treatment of the Schrödinger equation at leading order in the WKB framework. The resulting quantization condition yields approximate energy levels that capture the essential dynamics of quarkonium systems and demonstrate the effectiveness of the WKB method for modeling hadronic bound states.