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.
Quantum digital signature (QDS) ensures the authenticity, integrity, and non-repudiation of message transmission with information-theoretic security. However, most existing QDS protocols require users to maintain aligned reference frames, which is a complex and time-consuming process, especially in large-scale networks. To overcome this limitation, we propose a reference-frame-independent (RFI)-QDS protocol that eliminates the need for reference frame alignment by utilizing an RFI quantum key distribution technique. Our RFI-QDS protocol enhances signature rates and robustness by bypassing the reference calibration step. This advantage becomes particularly significant under conditions of large reference misalignment. Simulation results demonstrate that our protocol achieves significantly higher signature rates compared to traditional QDS schemes, even in the presence of severe reference misalignment.
Both irreversibility and incompatibility are important features of quantum channels. Irreversibility of quantum channels characterizes the fundamental limitation in reconstructing information from their outputs. This concept has traditionally been studied for individual channels in a global sense. In this work we generalize the conventional definition of reversible channels to relatively reversible channels, where a quantum channel is reversible relative to another one; thus it is in a relative sense. Incompatibility refers to the impossibility of simultaneously implementing certain pairs of quantum channels, and lies at the very heart of quantum theory. By leveraging the concept of complementary channels, we obtain a direct connection between relative reversibility and channel compatibility. We further propose a quantifier of channel irreversibility in terms of incompatibility between the complementary channels and the identity channel. To illustrate and compare the quantifier of irreversibility with some other quantifiers in the literature, we evaluate them for some prototypical channels. Our results provide insights into the interplay between irreversibility and incompatibility, which may have potential applications in quantum error correction and the resource theory of incompatibility.
Synchronization transmission describes the emergence of coherence between two uncoupled oscillators mediated by their mutual coupling to an intermediate one. In classical star networks, such mediated coupling gives rise to remote synchronization—where nonadjacent leaf nodes synchronize through a nonsynchronous hub—and to explosive synchronization, characterized by an abrupt collective transition to coherence. In the quantum regime, analogous effects can arise from the interplay between 1:1 phase locking and 2:1 phase-locking blockade in coupled spin-1 particles. In this work, we investigate a star network composed of spin-1 particles. For identical oscillators, symmetric and asymmetric dissipation leads to distinct transmission behaviors: remote synchronization and quasi-explosive synchronization appear in different coupling regimes, a phenomenon absent in classical counterparts. For nonidentical networks, we find that at large detuning remote synchronization emerges in the weak-coupling regime and evolves into quasi-explosive synchronization as the coupling increases, consistent with classical star-network dynamics. These findings reveal the rich dynamical characteristics of mediated quantum synchronization and point toward new possibilities for exploring synchronization transmission in larger and more complex quantum systems.
We show that the harmonic and Kepler–Coulomb potentials, supplemented by a singular 1/r2 term, can coexist exactly in an N-dimensional space with constant curvature. Unlike existing approaches, which treat these interactions separately or rely on analytical or numerical approximations, our construction is based on a conformal metric that preserves supersymmetry through shape invariance. This coexistence is possible only under the requirement that the effective curvature parameter satisfies τ2 > 0, which leads to a unique critical dimension, N = 4, where dynamical compatibility is maximized, even for vanishing angular momentum ℓ = 0. This result shows that curvature acts not merely as a kinematical parameter, but as an active geometric mediator, capable of restoring a hidden symmetry that is broken in flat Euclidean space.
Similar to the covalent bond in chemical molecules induced by shared electrons, we proposed in Chen (2022 Commun. Theor. Phys. 74 125201) a hadronic covalent bond induced by shared light quarks to explain Tcc(3875) and the deuteron. In this paper we improve and extend this mechanism to explain Zc(3900), which is bound by the shared light quark–antiquark pair along with sea quark–antiquark pairs from the vacuum. Our analysis is based on the following forward and backward reasoning: a hadronic molecule exists, iff the attraction between its components is strong enough, iff the wave functions of its components significantly overlap with each other, iff the Pauli principle is well satisfied among all the shared quarks and antiquarks. Additionally, X(3872) is so unique that we need to further consider the annihilation of the shared light quark–antiquark pair, just in line with the reasoning that the creation and annihilation of sea quark–antiquark pairs should be given equal consideration. Both the ‘creation’ and ‘annihilation’ molecular bonds exist only in the strong interaction, not in the electromagnetic interaction, and they provide a quasi-static low-energy platform for studying quantum chromodynamic confinement.
The electronic stopping power of magnesium (Mg) for protons is studied over a wide range of velocities by performing real-time time-dependent density functional theory (TDDFT) simulations. The electronic stopping power of Mg for high-velocity protons traveling along both channeling and off-channeling trajectories is calculated, and the microscopic mechanism responsible for the inner-electron excitation of Mg is revealed. In the low-velocity range (v < 1 au), the stopping power calculated from the channeling geometry aligns closely with the experimental measurements. It captures the departure from the linear relationship between the stopping power and proton velocity, which is attributed to charge exchange effect between protons and host electrons. The threshold velocities for 2p and 2s electron excitation of Mg for protons were found by TDDFT calculations. In the high-velocity range, the dependence of 2s-electron excitation on the impact parameter was investigated. Compared to channeling stopping, the off-channeling stopping exhibits significant enhancement. Furthermore, the impact of ion trajectories on electron excitation was also investigated. The results confirmed that the 3s electron excitation makes a significant contribution, and the decrease of the impact parameter enhances the inner electron excitation.
This work provides an analysis of pT spectra for identified hadrons generated during gold–gold collisions at a center-of-mass energy ($\sqrt{{s}_{NN}}$) of 11.5 GeV. The data, recorded by the STAR detector at the Relativistic Heavy Ion Collider, is evaluated using predictions from phenomenological models. Specifically, we compare the outcomes of Monte Carlo simulations from Pythia 8.3 and EPOS (comprising EPOS4 and EPOSLHC) with experimental observations. Our investigation focuses on π±, K±, and (anti-)proton spectra measured at mid-rapidity (∣y∣ < 0.1) across nine distinct centrality classes. In the case of π±, EPOS4 model shows good agreement with the data only in the low pT region. However, it successfully reproduces the results across the entire pT range for the last three centrality classes for pions yields. In the case of K±, EPOS4 exhibit good agreement with the experimental data. For proton and (anti-)proton, this model mostly underestimates in high-pT region, likely due to the reduced interaction volume and lower rescattering probability. In contrast, Pythia 8.3 often overpredicts pion yields and provides consistent representations for kaons and for (anti-)protons, Pythia 8.3 and EPOSLHC fails to describe the data. Pythia 8.3 mostly overestimates the data in the case of proton. EPOS4 demonstrates a good description of pion spectra compared to Pythia 8.3, largely attributable to its inclusion of hadronic rescattering effects. Meanwhile, EPOSLHC shows better alignment with experimental data in the case of kaons and proton for the entire pT range while for pions it also better reproduced the result at higher pT only. At higher pT, EPOSLHC exhibits a suppression relative to the experimental data, indicating limitations of the model description in a momentum region where collective flow effects are expected to be minimal. EPOS4 and EPOSLHC outperform Pythia 8.3, primarily due to their ability to incorporate correlated flow dynamics and hadronic rescattering effects. In contrast, Pythia 8.3 lacks these mechanisms, leading to less precise spectral descriptions. None of the models accurately replicate the experimental data for the (70–80)% centrality class likely due to the absence of collective effects and the increased role of non-equilibrium dynamics in these events. Additionally, the extracted freeze-out parameters indicate a rise in effective temperature and a decrease in the non-extensive parameter with increasing centrality. These trends suggest greater system excitation and more rapid thermal equilibration in highly central collisions.
Recent measurements of the scalar spectral index ns reported by the Atacama Cosmology Telescope (ACT) appear to be in tension with the predictions of many standard inflationary models. In this work, we show that constant-roll tachyon inflation can be compatible with the latest observational data. We consider the constant-roll condition with the slow-roll parameter ηV = 2V,TT/V2 being a constant. To be consistent with the 1σ constraints from the combined P-ACT-LB-BK18 data, the parameter ηV must lie within the range −0.016 < ηV < −0.0096. For consistency with the 2σ constraints, the allowed range is extended to −0.025 < ηV < 0.00063. These results indicate that constant-roll tachyon inflation provides a viable alternative to conventional models under the current observational constraints.
Primordial black holes (PBHs), a major candidate for dark matter, have been extensively constrained across most mass ranges. However, PBHs in the mass range 1017–1021 g remain a viable explanation for all dark matter. In this study, we use observational data from the Hard X-ray Modulation Telescope (Insight-HXMT) to refine constraints on PBHs within the mass range 2 × 1016–5 × 1017 g. Our analysis explores three scenarios: directly using observational data, incorporating the astrophysical background model, and employing the power-law spectrum with an exponential cutoff. Our research results indicate that although Insight-HXMT does not have an advantage in the first two scenarios, when considering the power-law model, its exceptional sensitivity in the hard X-ray regime and sufficiently high upper energy limit significantly strengthen the constraints on PBHs with masses greater than 1017 g compared to previous limits. Furthermore, the exclusion limit for PBHs as dark matter has reached 4 × 1017 g, which is comparable to the current threshold.
This work focuses on particle production described by a nonminimally coupled model during inflation. In this model, three parameters determine the characteristic frequency and strength of the induced gravitational waves (GWs). Considering the impact of particle production on inflation, we identify the parameter values that generate the strongest GWs without violating the slow-roll mechanism at the cosmic microwave background (CMB) scale. However, even with such extreme parameters, the power spectrum of induced GWs is only about 0.3% of that of vacuum GWs. This contribution remains insignificant when identifying the primary source of the detected CMB B-mode polarization. Furthermore, when our results are integrated with the constraints driven by P + ACT + LB + BK18, the contribution of induced GWs at CMB scales becomes negligible. In contrast, their impact on the scalar spectral index ns proves significant. For a range of parameter values, the Starobinsky inflation model yields predictions for ns that are consistent with the measurements obtained from P+ACT+LB+BK18.
The classical ensemble model (CEM) was applied to study the double ionization (DI) yield and correlated dynamics of electron pairs during non-sequential double ionization (NSDI) of oxygen molecules exposed to a counter-rotating two-color elliptically polarized (TCEP) laser field. Numerical simulations revealed a gradual reduction in the DI yield with increasing angle between the major axes of the two elliptically polarized laser components. This angular dependence arises from asymmetric suppression effects that the laser field exerts on the potential barrier of the diatomic molecule, with larger angles decreasing the efficiency of the barrier suppression. Concurrently, as molecular orientation angles increase, the increased travel time of the rescattering electron enhances recollision energies, thereby shifting the joint temporal distribution of ionization and recollision events toward diagonal alignment and altering the dominant NSDI pathways in oxygen molecules.
A theoretical investigation is presented on the generation of terahertz (THz) radiation through the nonlinear interaction of a cubic frequency chirped Hermite–Cosh–Gaussian (HChG) laser beam with an underdense plasma. The structured intensity profile of the HChG beam, characterized by its mode index, beam width parameter, decentered parameter, and Cosh envelope, enables enhanced spatial confinement and field gradients, which are very significant for efficient THz generation. The incorporation of a cubic frequency chirp modulates the temporal phase of the laser pulse, thereby increasing the interaction duration between the laser and plasma electrons. This leads to a stronger ponderomotive force, which drives a transient nonlinear current density at the beat frequency, resulting in the emission of THz radiation. Analytical expressions for the nonlinear current and THz field amplitude are derived, and parametric analysis reveals that the THz output is highly sensitive to the chirp coefficient, laser intensity, mode index, and plasma density profile. We found that higher-order spatial modes and carefully adjusted beam positioning (decentering) further enhance THz output. The best results were achieved at a lower chirp value (b = 0.00099), which outperformed traditional linear and quadratic chirping. This study demonstrates that cubic chirping significantly enhances the THz conversion efficiency compared to linear and quadratic chirps, offering a tunable and high-intensity THz source for applications in spectroscopy, imaging, wireless communication, ultrafast material characterization, and medical diagnostics.
We propose to trap circular Rydberg atoms (CRAs) via a ponderomotive potential well formed by a superimposed vortex light beam. We analytically calculate the ponderomotive potential energy for a Bessel vortex light beam. We work out a corrected version of the classical circular orbit approximation for a CRA which fits the exact result much better than the usual approximation. We reveal the three-dimensional characteristics of the potential well for some benchmark values of the CRA principal quantum number and beam parameters such as the frequency, the opening angle and topological charge of the vortex. We investigate how we can achieve similar trapping effects for different principal quantum numbers by varying beam parameters. The potential provides a lattice structure along the beam axis where one CRA could be trapped at each lattice site.
We analyse the eigenvalues of the Schrödinger equation with the Hellmann potential obtained by means of the generalized parametric Nikiforov–Uvarov (NU) method under the Greene–Aldrich approximation. We show that the NU eigenvalues yield the correct result when the screening parameter δ vanishes but their slope at δ = 0 differs considerably from the exact one. In addition, the NU eigenvalues behave pathologically at large values of the radial quantum number n and it is necessary to restrict its values to $0\leqslant n\lt {n}_{{\rm{\max }}}$.
The Wiener path integral framework is proposed to model military combat dynamics by incorporating the neglected stochastic effects to the Lanchester’s square law. This framework is applied to evaluate the empirical 3:1 combat rule, which posits that an attacker requires a threefold force superiority to achieve victory. Specifically, the attacker’s winning probability is computed utilizing a semi-analytical Rayleigh–Ritz method. Numerical results demonstrate that the validity of the rule critically depends on specific parameter regimes, primarily contingent upon the relative combat effectiveness ratio between the opposing forces and the tolerance for attrition. This work establishes a physics-informed theoretical bridge between statistical mechanics and military operations research for analyzing uncertain combat systems.
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.
Resistance and impedance networks have applications in many disciplines and can be used for simulation research. Consider a famous m × n Möbius-strip (MS) circuit network model, which is a special topology structure with unique one sidedness, non orientability, and edge characteristics that provide novel modeling ideas for network science. The study of its electrical characteristic formula has been challenging for over a hundred years. This article establishes a new research theory and uses the recursive-transform method based on node voltage to construct a 2D difference equation model. In solving the matrix equation, a new matrix transform technique is established to ingeniously transform the 2D equation into a 1D difference equation. The electric potential function and effective resistance formula of the m × n MS network are derived. Visual images of the electric potential function and effective resistance of the resistance lattice were drawn using Matlab drawing tools. As a byproduct of this study, the article discovered new mathematical identities in the comparison of results obtained from two different methods. The analytical formula for electrical characteristics derived from the article can provide a new theoretical basis and research techniques for related disciplines.
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 Hm without bond–charge interactions. When the condition for ${({\eta }^{\dagger })}^{N}| 0\rangle $to be an eigenstate of the Hubbard-type Hamiltonian Hm is satisfied, we demonstrate that there are additional states, distinct from ${({\eta }^{\dagger })}^{N}| 0\rangle $, which are also exact eigenstates of Hm. Our results enhance the understanding of Hubbard models on general graphs, both with and without bond–charge interactions.
We aim to clarify the confusion and inconsistency in our recent works (Luo et al 2023 Commun. Theor. Phys. 75 095702; Liang et al 2024 Phys. Rev. B 110 075125), and to address the incompleteness therein. In order to avoid the ill-defined nature of the free propagator of the gauge field in the ordered states of the t–J model, we adopted a gauge fixing that was not of the Becchi–Rouet–Stora–Tyutin (BRST) exact form in our previous work (Liang et al 2024 Phys. Rev. B 110 075125). This led to the situation where Dirac’s second-class constraints, namely, the slave particle number constraint and the Ioffe–Larkin current constraint, were not rigorously obeyed. Here we show that a consistent gauge fixing condition that enforces the exact constraints is BRST-exact in our theory. An example is the Lorenz gauge. On the other hand, we prove that although the free propagator of the gauge field in the Lorenz gauge is ill-defined, the full propagator is still well-defined. This implies that the strongly correlated t–J model can be exactly mapped to a perturbatively controllable theory within the slave particle representation.
