We investigate the application of the on-shell unitarity method to compute the anomalous dimensions of effective field theory operators. We compute one-loop anomalous dimensions for the dimension-7 operator mixing in low-energy effective field theory (LEFT). The on-shell method significantly simplifies the construction of scattering amplitudes. By leveraging the correspondence between the anomalous dimensions of operator form factors and the double-cut phase-space integrals, we bypass the need for direct loop integral calculations. The resulting renormalization group equations derived in this work provide crucial insights into the scale dependence of the LEFT dimension-7 Wilson coefficients, which will aid in precision experimental fitting of these coefficients.

In the framework of general relativity (GR), gravitational waves (GWs) travel at the speed of light across all frequencies. However, massive gravity and weak equivalence principle (WEP) violation may lead to frequency-dependent variations in the propagation speed of GWs, which can be examined by comparing the theoretical and observed discrepancies in the arrival times of GW signals at various frequencies. This provides us with an opportunity to test these theories. For massive gravity, we consider that gravitons may have a nonzero rest mass. For WEP violations, we hypothesize that different massless particles exposed to the same gravitational source should exhibit varying gravitational time delays. The gravitational time delay induced by massive gravitational sources is proportional to γ + 1, where the parameter γ = 1 in GR. Therefore, we can quantify these two deviations using phenomenological parameters m_g and ∣Δγ∣, respectively. In this study, we use selected GW data from binary black hole coalescences in the LIGO-Virgo catalogs GWTC-2.1 and GWTC-3 to place constraints on the parameters m_g and ∣Δγ∣. We also compute Bayes factors for models that assume the existence of graviton mass and WEP violation compared to the standard GW model, respectively. The absolute value of the natural logarithm of the Bayes factor is generally less than two. Our analysis reveals no significant preference for either model. Additionally, the Bayes factors between these two models do not provide obvious evidence in favor of either one.

We study the thermoelectric transport of a series-coupled double quantum dots (SDQDs) system, based on the hierarchical equations of motion approach. The thermocurrent as a function of the energy level of QDs gives rise to a sign-changing phenomenon. The temperature difference between the two leads can enhance the thermocurrent. Moreover, the sign changing also generates in thermocurrent as a function of temperature due to the transition from the many-body Kondo resonant tunneling process to the single electron process of the SDQDs system. The inter-dot coupling strength between two QDs not only affects the value of the thermocurrent but also influences the characteristic temperature at which the sign changing of thermocurrent emerges. In a weak coupling regime, the thermocurrent firstly is enhanced by inter-dot coupling strength due to the ‘t-enhanced Kondo effect’ and then decreases with inter-dot coupling strength due to the effective antiferromagnetic interaction between the two QDs. In the middle coupling regime, the forming coherence bonding and antibonding orbitals channels and the residual Kondo effect co-dominate the transport process. The thermocurrent firstly decreases, then increases, and finally decreases with temperature. However, the thermocurrent shows a transition from increasing to decreasing behavior with temperature in the strong coupling regime. Although the inter-dot coupling strength t has a complex impact on the SDQDs system, the characteristic temperature k_BT_c, at which a sign changing appears, indicates a quantitative relationship with the value of the inter-dot coupling strength t by an identical amount of the Kondo correlation being partially destroyed.

This paper investigates the physical significance of the infinitely many K- and τ-symmetries associated with the soliton and complex solutions of the sine-Gordon (sG) equation. It is shown that the K-symmetries are linear combinations of wave center translation symmetries, while the τ-symmetries combine both wave center translation and wave number translation symmetries. Only a subset of the K- and τ-symmetries are independent, indicating that these symmetries are not incomplete. A special one-soliton solution of the sG equation is derived by using the generalized symmetries.

We investigate phase-controlled bound states in a one-dimensional photonic waveguide coupled to an artificial giant atom at two distant sites. Specifically, we identify the bound state out of the continuum (BOC) and the bound state in the continuum (BIC) and derive the exact existence condition for the BOC. Furthermore, we analytically determine the BIC’s frequency and photonic distribution profile. Remarkably, our analysis reveals quantum beats in both atomic and photonic dynamics, arising from coherent oscillations between the BIC and BOC. These results establish a novel approach for manipulating waveguide quantum electrodynamics via engineered bound states, with potential applications in quantum information processing.

This study investigates the dimensionless quasi-geostrophic potential vorticity (QG-PV) equation with external sources. Employing the Gardner–Morikawa transformation and weakly nonlinear perturbation expansion, we derive the nonlinear Boussinesq equation with external sources. We demonstrate the existence of explicit zero-order and first-order Wronskian solutions for the model equation when α₄ = 0. Furthermore, using a modified Jacobi elliptic function method, we obtain soliton-like solutions for both α₄ = 0 and α₄ ≠ 0. Analysis of these solutions reveals that the generalized β-plane approximation and shear flow are significant factors in inducing nonlinear Rossby waves, and that external sources play a crucial role in influencing Rossby wave behavior.

This research aims to examine the (1+1)-dimensional Schrödinger–Maxwell–Bloch (SMB) model, which is of great significance for the study of the dynamic properties of optical solitons in the media. We obtain the exact analytical soliton solutions for the given model using the new Kudryashov’s method, which helps to reveal various forms of the nonlinear waves. The proposed approach yields explicit localized wave structures, including bright soliton and dark-bright composite profiles associated with the field components of the SMB system. These solutions describe stable localized pulses and their accompanying field interactions in resonant nonlinear optical media. These solutions are shown using 3D plots, 2D plots, contour plots, as well as polar plots to gain a better understanding of their spatiotemporal properties. These plots also help to show the overlap of the temporal pulses. In addition to the solution development, the dynamical properties of the system are also rigorously investigated. Bifurcation plots are used to explore the stability properties of the system for varying important parameters. Chaotic properties are explored using numerical techniques such as simulations, including properties such as multistability, initial value sensitivity, recurrence plots, and power spectra. These topics illustrate in more detail the complex properties that are inherent in the SMB system. These topics not only discuss properties of optical solitons but could also provide research opportunities in the area of nonlinear optics, optical communication, or laser physics for which controllable soliton propagation is critical. This study provides a uniting methodology that embeds exact solutions and nonlinear dynamical systems analysis to present a well-rounded approach for the study of solitons and related phenomena in the SMB system.

The theory of statistical physics relies on ergodicity, whereby in large or interacting systems lacking integrability, trajectories eventually explore nearly all points in the phase space. It has been believed that chaotic dynamics provide a possible pathway to ergodicity. Here, we examine the phase space density distributions and their recurrence in the harmonic oscillator, the linear and nonlinear Mathieu equations, the Lorenz attractor, and the Nosé–Hoover model. We show that in models with periodic or quasiperiodic dynamics, sharp peaks can be found in the phase space density distributions. However, for the chaotic dynamics, their distributions display totally different behaviors. We understand these differences using recurrence plots. Our results show that while chaotic dynamics provide an efficient way for the trajectory to explore a large portion of the phase space, which is necessary for ergodicity, the chaotic dynamics are not sufficient for this goal. For instance, despite the Nosé–Hoover model being chaotic, it is not sufficiently large for ergodicity. Therefore, our results may lead to an important conclusion, which is that ergodicity may be realized from large chaotic systems. These findings in these simple models can be explored in experiments in the future, which may provide some key insights into ergodic dynamics.

Voting is an important social activity for expressing public opinions. By conceptually considering a group of voting agents to be intelligent matter, the impact of real-time information on voting results is quantitatively studied by an intelligent Ising model, which is formed by adding nonlinear instantaneous feedback of the overall magnetization to the conventional Ising model. In the new model, the interaction strength becomes a variable depending on the total magnetization rather than a constant, which mimics the scenario that the decision of an individual during vote influenced by the dynamically changing polling result during the election process. Our analytical derivations along with Monte Carlo simulations reveal that, with a positive feedback, the intelligent Ising model exhibits phase transitions at any finite temperatures, a feature lacked in the conventional one-dimensional Ising model. In all dimensions, by varying the feedback strength, the system changes from going through a second-order phase transition to going through a first-order phase transition with increasing temperature, and the two types of phase transitions are connected by a tricritical point. This study on the one hand demonstrates that the intelligent matter with a nonlinear adaptive interaction can exhibit qualitatively different phase behaviors from conventional matter, and on the other hand shows that, during voting, even unbiased feedback may possibly induce spontaneous symmetry breaking, leading to a biased outcome where one side of the vote becomes favored.

For even–even nuclei ^180−184Yb, ^182−186Hf and ^184−188W located on an island of hexadecapole-deformation archipelago, the structure properties, especially under rotation, are reinvestigated by using the Hartree–Fock–Bogliubov–Cranking (HFBC) calculation with a fixed shape (e.g., the ground-state equilibrium shape). The equilibrium deformations, extracted from the potential energy surface, are calculated based on the phenomenological Woods–Saxon (WS) mean-field Hamiltonian within the framework of macroscopic-microscopic (MM) model. The impact of different deformation degrees of freedom on, e.g., single-particle levels, total energy, and moment of inertia (MoI), is revealed, especially concentrating on the hexadecapole-deformation effects and the quadrupole-hexadecapole coupling. Considering the axially hexadecapole deformation, the present calculations can reproduce available experimental data well, including the quadrupole deformations and moments of inertia. Interestingly, it is found that the impact of different deformation degrees of freedom on MoI exhibits a similar trend in the HFBC and rigid-body calculations though the latter ignores the pairing effects. Before starting or constructing a complex theory-model, to some extent, such a similarity can provide an alternative way of understanding the effect of, e.g., exotic deformations, on the MoI by the calculation of a simple rigid-body approximation. The present findings could offer insights into the static and dynamic effects of hexadecapole deformations, contributing valuable information for the corresponding research in nuclear structure and reaction.

We propose an effective surface plasmon resonance system designed to achieve both negative and positive Goos–Hänchen shifts in reflected light. This system comprises a metal film and an underlying medium, where the real part of the permittivity of the underlying medium must be less than unity. Surface plasmon polaritons can be excited at the lower surface of the metal when light is incident from the air onto the upper surface of the metal. The excitation of surface plasmon polaritons leads to the exploration of the Goos–Hänchen shift (G–HS). Control over the negative and positive (G–HS) is investigated via the wavelength of the incident light. The magnitude of the G–HS is strongly dependent on the incident wavelength. A remarkable enhancement of both negative and positive G–HS in the reflected light is achieved at certain wavelengths and incident angles. Our system paves the way for exploring different characteristics of optical switching and micro-sensors with very high precision.

White dwarfs, one of the compact objects in the Universe, play a crucial role in astrophysical research and provide a platform for exploring nuclear physics. In this work, we extend the relativistic mean field approach by using a Walecka-type quantum hadrodynamics model to capture the intricate structure of white dwarfs. We calculate nuclear properties, Coulomb energy, and photon energy within white dwarfs in a unified framework. By carefully calibrating the model parameters to align with nuclear matter properties, we successfully reproduce the structures of several elements in white dwarfs, such as the isotopes of C and ¹⁶O, except for the unnaturally deeply bound state ⁴He. Furthermore, we predict the characteristics of white dwarfs composed of atom-like units and the gravitational waves stemming from binary white dwarf inspirals incorporating tidal deformability contributions up to the 2.5 post-Newtonian order. These results shed light on the structure of white dwarfs and provide valuable information for future gravitational wave detection. This methodological advancement allows for a cohesive analysis of white dwarfs, neutron stars, and the nuclear pasta within a unified theoretical framework.

The chiral gravitational wave background (GWB) can be produced by axion-like fields in the early universe. We perform parameter estimation for two types of chiral GWB with the LISA-Taiji network: axion-dark photon coupling and axion-Nieh–Yan coupling. We estimate the spectral parameters of these two mechanisms induced by the axion and determine the normalized model parameters using the Fisher information matrix. For highly chiral GWB signals that we choose to analyze in the mHz band, the normalized model parameters are constrained with a relative error less than 6.7% (dark photon coupling) and 2.2% (Nieh–Yan coupling) at the one-sigma confidence level. The circular polarization parameters are constrained with a relative error around 21% (dark photon coupling) and 6.2% (Nieh–Yan coupling) at the one-sigma confidence level.

This study delves into the role of the neuromuscular junction in communication between nerves and muscles, as well as the importance of sarcomeres in muscle contraction. A mechanical device and circuit model is developed to simulate the movement of sarcomeres and the biophysical properties of skeletal muscles, including membrane potential and channel currents. The model integrates electromagnetic, kinetic, and elastic potential energy, which is verified by Helmholtz’s theorem. By using memristors to simulate the neuromuscular junction, the coupling of neuronal circuits with muscle cell circuits is achieved, and dynamic analysis is conducted. Adjusting Hamiltonian energy parameters can modulate oscillation patterns and beam displacement, optimizing the coupling strength between neurons and muscle cells. The study demonstrates that by manipulating energy ratios, it is possible to control the interactions between muscle cells.

This paper presents a geometric perspective that connects reciprocal transformations with multidimensional integrable deformations. By interpreting conservation laws as closed 1-forms, we formalize reciprocal transformations as induced local diffeomorphisms on the jet bundle. This allows us to characterize higher-dimensional deformations as systematic fiber bundle extensions, where fiber coordinates are generated by potential functions of the conservation laws. This perspective provides an interpretation for the covariant lifting of Lax pairs to higher dimensions and reveals that auto-Bäcklund transformations are composite diffeomorphisms. These results are applied to several classical integrable models.

Gravitational collapse and bubble evolution in the asymptotic Friedmann–Lemaître–Robertson–Walker (FLRW) Universe is an intriguing and intricate problem. We systematically analyze the dynamics of contact Schwarzschild–FLRW (McVittie) spacetimes, focusing on their general junction conditions and introducing a novel function to simplify the extrinsic curvature and surface stress–energy tensor. Both static and dynamic scenarios are explored, including special cases such as Schwarzschild, FLRW, and Einstein–Straus configurations using our general framework. Numerical calculations further investigate the evolution of concentric McVittie spacetimes under various initial conditions, incorporating Λ-CDM cosmological models to better reflect realistic cosmic backgrounds. These results offer deep insights into the interplay between the McVittie mass parameter, initial peculiar velocity, and the influence of dark energy, providing a unified perspective for understanding gravitational collapse and bubble evolution in cosmology and astrophysics.

This paper explores the application of Whitham modulation theory to the third-order focusing Kaup–Newell model, offering a complete classification of solutions for step-like initial value problems. Using the finite-gap integration method, we derive periodic solutions and the corresponding Whitham modulation equations. By analyzing the distribution of Riemann invariants, we identify the fundamental wave structures emerging from the step-like initial value problem. Furthermore, we provide a complete classification of solutions for this problem. Our results demonstrate that Whitham modulation theory serves as an effective analytical framework for studying initial value discontinuities in the third-order focusing KN model, offering new insights into its nonlinear dynamical behavior. Moreover, the direct numerical simulations show remarkable agreement with the results from Whitham modulation theory.

Official and civil information, as distinct information sources, significantly influence public behavior and the dynamics of epidemic transmission. In this paper, we propose a three-layer ${U}_{1}{A}_{1}{U}_{1}-{U}_{2}{A}_{2}{U}_{2}-SIS$ coupled model to analyze the co-evolution process of official information dissemination, civil information dissemination and epidemic transmission, considering the interdependencies between the information dissemination channels. The first layer describes the official information dissemination process. The second layer models the civil information dissemination process, considering the effects of perceived risk costs and the role of the correlation between official and civil information. The third layer represents the epidemic transmission process, highlighting the impact of the correlation between official and civil information on epidemic transmission. Then, using the microscopic Markov chain approach, we describe the information-epidemic coupled dynamics and derive the epidemic outbreak threshold. Our research demonstrates that a stronger positive correlation between official and civil information raises the epidemic threshold and suppresses the scale of epidemic transmission. Furthermore, individuals’ adoption of civil information should involve a more thorough assessment of the infection risk based on their personal circumstances, which can contribute to more effective epidemic control. Moreover, enhancing infected individuals’ accurate comprehension of official information can effectively curb the transmission of the epidemic. Our study highlights the importance of both official and civil information dissemination in epidemic management and provides insights for policymakers in developing effective public health and communication strategies.

We have analyzed magnetic order in the one-dimensional Kondo lattice with classical localized spins. To identify relevant low-energy configurations, we combine the exact diagonalization of the electronic system with a dissipative evolution, described by the Landau–Lifshitz-Gilbert equation. We find that spiral states always relax into a more complex form of noncollinear order, characterized by a periodic modulation of the relative angles between neighboring spins. A finite-size scaling analysis shows that the amplitude of the modulation and the gain in free energy remain finite in the thermodynamic limit. Importantly, the wavelength of the modulation is determined by the Fermi wavevector of the unperturbed spiral. This suggests that complex noncollinear order originates from an instability of the unperturbed spirals, which, in the presence of a weak pairing term, may hinder topological superconductivity. Our final phase diagram is obtained by comparing the modulated spiral states with various complex collinear configurations proposed in the literature.

This research paper seeks to investigate the characteristics of almost Riemann solitons and almost gradient Riemann solitons within the framework of generalized Robertson–Walker (GRW) spacetimes that incorporate imperfect fluids. Our study begins by defining specific properties of the potential vector field linked to these solitons. We examine the potential vector field of an almost Riemann soliton on GRW imperfect fluid spacetimes, establishing that it aligns collinearly with a unit timelike torse-forming vector field. This leads us to express the scalar curvature in relation to the structures of soliton and spacetime. Furthermore, we explore the characteristics of an almost gradient Riemann soliton with a potential function ψ across a range of GRW imperfect fluid spacetimes, deriving a formula for the Laplacian of ψ. We also categorize almost Riemann solitons on GRW imperfect fluid spacetimes into three types: shrinking, steady, and expanding, when the potential vector field of the soliton is Killing. We prove that a GRW imperfect fluid spacetime with constant scalar curvature and a Killing vector field admits an almost Riemann soliton. Additionally, we demonstrate that if the potential vector field of the almost Riemann soliton is a ν(Ric)-vector, or if the GRW imperfect fluid spacetime is ${{ \mathcal W }}_{2}$-flat or pseudo-projectively flat, the resulting spacetime is classified as a dark fluid.

The observed identical π7/2⁻[514] band and near-identical π1/2⁻[521] band in ²⁵¹Md and ²⁵⁵Lr are investigated using the cranked shell model (CSM) with the particle-number-conserving (PNC) pairing method. The experimental kinematic moments of inertia (MOIs) J⁽¹⁾ for each band are reproduced well by the PNC-CSM calculations. A remarkable identity is exhibited for the variation of the calculated MOIs J⁽¹⁾ versus the frequency between ²⁵¹Md and ²⁵⁵Lr, which is attributed to the identical contributions of the alignment from the blocked proton orbitals π[514]7/2 (π[521]1/2) in ²⁵¹Md and ²⁵⁵Lr. The slight differences of J⁽¹⁾ at high frequency ℏω > 0.2 MeV for the near-identical π1/2⁻[521] band are due to the contributions of the direct term j⁽¹⁾(μ) and the interference term j⁽¹⁾(μν) based on the neutron orbital ν9/2⁻[734]. The B(E2) values are lower in ²⁵¹Md than in ²⁵⁵Lr while the pairing gaps are almost the same for the π7/2⁻[514] and π1/2⁻[521] bands. The behaviors of the B(E2) values (pairing gaps) versus frequency are predicted to exhibit a remarkable similarity in ²⁵¹Md and ²⁵⁵Lr.

In order to investigate physically meaning localized nonlinear waves on the periodic background defined by Weierstrass elliptic ℘-function for the (n + 1)-dimensional generalized Kadomtsev–Petviashvili equation by Darboux transformation, the associated linear spectral problem with the Weierstrass function as the external potential is studied by utilizing the Lamé function. The degenerate solutions of the nonlinear waves have also been obtained by approaching the limits of the half-periods ω₁ and ω₂ of ℘(x). At the same time, the evolution and nonlinear dynamics of various nonlinear waves under different parameter regimes are systematically discussed. The findings may open avenues for related experimental investigations and potential applications in various nonlinear science domains, such as nonlinear optics and oceanography.

In this study, we propose that many different thermodynamic modeling approaches, including the general equation for the non-equilibrium reversible-irreversible coupling (GENERIC), Onsager's variational principle, the energetic variational approach, and classical irreversible thermodynamics, can all be cast into the gradient-conservative structure (GCS). GCS enjoys many nice mathematical properties, has close connection with the large deviations principle and gradient flows in Wasserstein space, and fulfills laws of thermodynamics. Our results demonstrate that the GCS may serve as a unified theoretical framework to model various non-equilibrium thermodynamic processes.

Under study in this paper is a nonlinear Schrödinger equation with local and nonlocal nonlinearities, which originates from the parity-symmetric reduction of the Manakov system and has applications in some physical systems with the parity symmetry constraint between two fields/components. Via the Riemann-Hilbert method, the theory of inverse scattering transform with the presence of double poles is extended for this equation under nonzero boundary conditions (NZBCs). Also, the double-pole soliton solutions with NZBCs are derived in the reflectionless case. It is shown that the quasi-periodic beating solitons can be obtained when the double pole lies off the circle $\Gamma$ centered at the origin with radius $\sqrt{2}{q}_{0}$ (where q₀ is the modulus of NZBCs) on the spectrum plane. Moreover, using the improved asymptotic analysis method, the asymptotic solitons are found to be located in some logarithmic curves of the xt plane.

We investigate magnetic correlation in the triangular lattice Hubbard model using determinant quantum Monte Carlo simulations. Focusing on the role of next-nearest-neighbor hopping ${t}^{{\prime} }$ and electron filling ⟨n⟩, we demonstrate that regions of high density of states, particularly near van Hove singularity (VHS) points, significantly enhance short-range ferromagnetic correlations as measured by the uniform spin susceptibility χ(Γ). Specifically, χ(Γ), quantifying ferromagnetic fluctuations, is amplified at fillings corresponding to the VHS for a given ${t}^{{\prime} }$. Increasing the on-site Coulomb repulsion U further strengthens these ferromagnetic correlations, with a more pronounced effect at lower temperatures, and the observed ferromagnetic correlations are found to be short-ranged. Conversely, near half-filling ⟨n⟩ = 1.0, larger ${t}^{{\prime} }$ values promote antiferromagnetic (AFM) fluctuations, evidenced by an increase in χ(K). Our results reveal that ${t}^{{\prime} }$and filling act as effective tuning parameters for manipulating the competition between ferromagnetic and AFM fluctuations in the triangular lattice.

We argue that the hypothesis that positive-parity charm meson resonances exhibit a compact tetraquark structure has some clear tension with recent lattice results for the S-wave πD system for an SU(3) flavor symmetric setting. In particular, we show that such a diquark–anti-diquark tetraquark scenario would call for the presence of a state in the flavor $[\overline{{\bf{15}}}]$ representation, not seen in the lattice analysis. Moreover, we show that analogous lattice data in the axial-vector channel are even more sensitive to the internal structure of these very interesting states.

The paper considers applications of Rota–Baxter algebras to renormalization in quantum field theory and quantum integrability to obtain new solutions for the Yang–Baxter equations which can be studied by the method of Renormalization Group.

In this paper, we show a general procedure to nonlinearize bilinear equations by using the Bell polynomials. As applications, we obtain nonlinear forms of some integrable bilinear equations (in the sense of having three-soliton solutions) of the KdV type and mKdV type that were found by Jarmo Hietarinta in the 1980s. Examples of non-integrable bilinear equations of the KdV type are also given.

Among many types of quantum entanglement properties, the entanglement spectrum provides more abundant information than other observables. Exact diagonalization and density matrix renormalization group methods could handle the system in one-dimension properly, while in a higher dimension, it exceeds the capacity of the algorithms. To expand the ability of existing numerical methods, we take a different approach via quantum Monte Carlo algorithm. By exploiting the particle number and spin conservation, we realize an efficient algorithm to solve the entanglement spectrum in the interacting fermionic system. Taking the two-dimensional interacting Su–Schrieffer–Heeger (SSH) model as an example, we verify the existence of topological phase transition under different types of many-body interactions. The calculated particle number distribution and wavefunction of the entanglement Hamiltonian indicate that the two belong to distinct types of topological phase transitions.

In 2021, LHCb collaboration reported a very narrow state in the D⁰D⁰π⁺ mass spectrum just below the D^*+D⁰ mass threshold. We consider the influence of the Castillejo–Dalitz–Dyson (CDD) pole in the scattering amplitude to derive a general treatment for the two-body final state interaction near its threshold. The line shape (or the energy dependent event distribution) are then obtained, where the parameters can be fixed by fitting to the experimental data on the D⁰D⁰π⁺ mass spectrum. Within our method the data are quite well reproduced. The pole structure in the complex energy plane indicates that the T_cc state has a large portion of elementary degree of freedom (e.g. the compact tetraquark component) inside its hadron wave function. The compositeness as a measure of molecule component in its wave function is predicted to be $0.2{3}_{-0.09}^{+0.40}$. Clearly, the non-molecular component takes a non-negligible or even dominant portion.

Light sub-GeV dark matter (DM) particles up-scattered by high-energy cosmic rays (CRs) (referred to as CRDM) can be energetic and become detectable by conventional DM direct detection experiments. Nevertheless, current CRDM theoretical frameworks remain limited by model-dependent parameterizations, whereas the effective operators provides a model-independent computing framework. In this work, we systematically investigate the general relativistic DM-nucleus spin-independent interactions. We first construct effective operators for dark matter with spin up to two, i.e. spin-1/2 fermionic DM (χ), the scalar DM (φ), the vector DM (V_μ), spin-3/2 fermionic DM ($\Psi$) and spin-2 DM (T^μν). We then derive the CRDM flux and the nuclear recoil event rate based on these operators, and employ nuclear recoil data from the LUX-ZEPLIN (LZ) experiment to constrain all effective operators. We set stringent constraints on the CRDM-nucleon scattering cross section for sub-GeV DM. Especially, our results show that the exclusion limits from the spin-2 T^μν operator differ by as much as ten orders of magnitude from those calculated using constant cross section.

Coupled oscillator systems often exhibit collective dynamics as a consequence of their mutual heterogeneous interactions. Recent studies have highlighted the importance of shear diversity, an inhomogeneous pattern, in influencing the collective behavior of complex systems. Here, we investigate the quenching dynamics occurring within a network of limit-cycle oscillators that are globally coupled by taking into account both the shear diversity and the heterogeneous natural frequencies that are assumed to be statistically independent. Beyond the phase-only model considered in previous studies, we propose a general approach for identifying the critical criteria, demonstrating the instability of the incoherent state, by retaining the responses of both amplitudes and phases. This study advances the understanding of the role of heterogeneous couplings in interacting dynamical agents, offering valuable insights into the quenching phenomena observed in complex systems.

The Navier–Stokes (NS) equation with Coriolis force and density-dependent viscosity is an important physical model, which has been widely used to understand and analyze a wide array of phenomena, including behaviors of the Gulf stream, dynamics of hurricanes, operation of chemical reactors and functionality of rotating machines. In this paper, based on the matrix and curve integration techniques, we build a sufficient condition for the existence of Cartesian vector solutions u = b(t) + A(t)x for the N-dimensional NS equation, in which A satisfies appropriate matrix equations. Then, we discuss two special cases of A and thereby explicit analytical solutions are obtained. To shed light on these solutions, we give some illustrative examples. Among them, some examples form the generalization previously obtained by other authors and some examples are quite new. Finally, we analyze the properties of Cartesian vector solutions in a special case.

The existence of absolute parametric instability in an inhomogeneous plasma is revisited in a one-dimensional three-wave model. Non-resonant daughter waves are considered to match the conditions of radio-frequency (RF)-plasma interactions in magnetically confined plasma. Our model shows that such absolute instability has an extremely high threshold and cannot be induced for typical RF-plasma interactions, even if the linear growth rate of the instability achieves the level of ion-cyclotron frequency. As a result, we suggest that it is appropriate to neglect absolute instability when non-resonant daughter waves are involved.

In this study, we present a comprehensive analysis of a modified Frolov black hole (BH) model that incorporates two types of topological defects, a global monopole (GM) and a cloud of strings (CS). This composite BH solution is examined from multiple theoretical perspectives to explore the impact of these modifications on the BH’s geometric, thermodynamic and dynamical properties. We begin by studying the geometrical optics of the spacetime, focusing on the motion of null geodesics. Key features, such as the effective potential, photon sphere, the force acting on photons and the stability of circular photon orbits, are analyzed in detail. Our results show that the presence of GM and CS significantly affects the spacetime geometry and photon dynamics. In addition, the thermodynamic behavior of the modified BH is also investigated. We derive essential quantities such as the Hawking temperature and entropy, demonstrating how the inclusion of GM and CS leads to deviations from the standard thermodynamic relations observed in classical BH solutions. These deviations may offer valuable insights into quantum gravity and the role of topological defects in BH physics. Furthermore, we examine the BH shadow as an observational signature of the underlying geometry. Our analysis shows that the Frolov parameter tends to reduce the apparent size of the shadow, while the presence of topological defects, particularly GM and CS, enlarges it. In addition, we investigate the perturbative dynamics of the BH by studying both scalar (spin-0), fermionic (spin-1/2) and electromagnetic (spin-1) fields through the massless Klein–Gordon and Maxwell equations, respectively. Using the Wentzel–Kramers–Brillouin approximation, we compute the quasinormal modes (QNMs) for scalar and electromagnetic field perturbations. The results confirm the stability of the BH under small perturbations and show that the QNM frequencies and damping rates are strongly influenced by the Frolov parameter, electric charge, GM and CS.

We investigate Hubbard models with bond–charge interactions on general graphs. For a Hamiltonian H of such a model, we provide the condition on its parameters under which the η-pairing method can be employed to construct its exact eigenstates. We arrive at this condition by finding that the requirement for the η-pairing state ${({\eta }^{\dagger })}^{N}| 0\rangle $ to be an eigenstate of H is identical to the requirement for it to be an eigenstate of a Hubbard-type Hamiltonian H_m without bond–charge interactions. When the condition for ${({\eta }^{\dagger })}^{N}| 0\rangle $to be an eigenstate of the Hubbard-type Hamiltonian H_m is satisfied, we demonstrate that there are additional states, distinct from ${({\eta }^{\dagger })}^{N}| 0\rangle $, which are also exact eigenstates of H_m. Our results enhance the understanding of Hubbard models on general graphs, both with and without bond–charge interactions.

We show that in Schwarzschild equivalent mediums, the massless spin particles obey the same dynamical equation, from which we obtain remarkably simple formulae for the frequencies of the quasibound states. We find that the quasibound frequencies of different bosons can be identical at the same quantum number l, and the same is true of different fermions, but a quasibound frequency for bosons can never equal a quasibound frequency for fermions. These results mean that in Schwarzschild equivalent mediums with the quasibound-state boundary conditions, characteristics of electromagnetic waves are the same as those for all the massless bosonic waves, thereby allowing electromagnetic waves to simulate gravitational waves. Our predictions can be tested in future experiments, building upon the successful preparation of Schwarzschild equivalent mediums.

Our analysis is particularly motivated by its relevance to understanding compact object instabilities, gravitational collapse thresholds, and the formation of dense structures under the influence of modified gravity theories. The interplay of anisotropic pressures, perturbative dynamics, and modified gravity contributions offers insight into both the stable configuration of dense fluids and the mechanisms leading to dynamical instability. Such considerations directly contribute to the aims of high energy density profiles, particularly in modeling physical systems where extreme pressure, curvature, and matter interactions co-exist. We consider an axially symmetric, dense structure with anisotropic matter content and employ a specific equation of state (EoS) to examine the interplay between static and dynamic quantities via the adiabatic index. To address the complex dynamics of the collapse process, a perturbative scheme is utilized under Newtonian and post-Newtonian approximations, enabling a detailed examination of the stability and structural evolution of the system under the influence of the considered minimally coupled gravity. Our results demonstrate that hydrostatic equilibrium is maintained when effective pressure, gravitational, and anti-gravitational forces are balanced, while deviations from this balance initiate dynamical instability. Graphical representations of stable and unstable regimes are presented, revealing how the choice of gravity functions significantly affects the outcome. This work provides insight into the behavior of dense, self-gravitating configurations under modified gravity, offering broader implications for the modeling of compact astrophysical objects and contributing to the understanding of gravitational collapse in energy density regimes.

Using a model-independent Gaussian process (GP) method to reconstruct the dimensionless luminosity distance D and its derivatives, we derive the evolution of the dimensionless Hubble parameter E, the deceleration parameter q, and the state parameter w of dark energy. We utilize the PantheonPlus, SH0ES, and Gamma Ray Burst (GRB) data to derive the dimensionless luminosity distance D. Additionally, we employ observational H(z) data (OHD) and baryon acoustic oscillations (BAO) from the Dark Energy Spectroscopic Instrument (DESI) Data Release 2 (DR2) to obtain the first derivative of the dimensionless luminosity distance ${D}^{{\prime} }$. To obtain the reconstructed D and ${D}^{{\prime} }$, we utilize the fiducial value from each dataset, with particular emphasis on the varying H₀. According to the reconstruction results obtained from PantheonPlus+SH0ES+GRB+OHD and PantheonPlus+SH0ES+GRB+OHD+DESI data, we find that E is consistent with the predictions of the $\Lambda$CDM model at a 2σ confidence level within the redshift range of z < 2. However, the reconstruction results for q exhibit deviations from the $\Lambda$CDM model in the range of z < 0.3. Furthermore, we observe that the mean value of w exhibits evolving behavior, transiting from w < -1 to w > -1 around ${z}_{{\rm{wt}}}=0.46{4}_{-0.120}^{+0.235}$. Combining data from DESI DR2 can slightly enhance the accuracy of our constraints.