Explosive synchronization (ES) describes an abrupt and hysteretic transition from incoherence to collective order and has been widely studied in static networks. Here, we show that temporal variability of network connectivity can fundamentally reshape this transition. We investigate inertial Kuramoto oscillators evolving on stochastically rewired random networks, where links are continuously replaced at controlled rates, allowing us to tune the interplay between inertia and topological dynamics. Our results reveal that temporal rewiring can both induce and suppress ES depending on the network density and the switching timescale. Sparse networks display ES only under very slow or very rapid switching, whereas denser networks exhibit robust explosive transitions across a broad parameter range. Increasing the rewiring probability generally promotes abrupt synchronization, but excessively frequent rewiring weakens hysteresis and reduces bistability. A systematic exploration across different degrees confirms that ES is most prominent when moderate-to-high rewiring probability is combined with rapid switching, whereas small rewiring probability favors continuous transitions. These findings demonstrate that temporal randomness is not merely a perturbation but a key control mechanism for abrupt collective behavior, representing how time-varying connectivity governs the onset, robustness, and disappearance of ES in dynamical networks.
In this paper, a generalized (3+1)-dimension variable-coefficient nonlinear evolution equation is investigated, which serves as a model for describing nonlinear wave behaviors in shallow water, ion-acoustic wave fluid mechanics and plasma physics. The Painlevé integrability is tested by the Weiss, Tabor and Carnevale (WTC) method with the simplified form of Krustal. The bilinear form of the equation is derived through the application of the Hirota bilinear method. Building on the bilinear equation, a broad range of analytical solutions are then obtained, including X-shaped and Y-shaped soliton solutions, lump solution, breather solution, and interaction solutions. In addition, another type of soliton solution, periodic solution, and ratio of trigonometric functions are derived.
The potential modified Korteweg–de Vries (pmKdV) equation possesses an infinite number of symmetries; however, the physical implications of these symmetries remain unexplored. Recent improvements have successfully elucidated that the physical significance of the infinite symmetries are related to wave number translation and wave center translation invariance. Following the ideas of these results, this paper aims to investigate the physical meanings associated with the infinite symmetries linked to the n-soliton solutions of the pmKdV equation. The findings indicate that the K-symmetries are related to the translational invariance of the wave center, while the τ-symmetry is associated with combined translational symmetries of both the wave center and wave number. Furthermore, these infinitely many symmetries are not entirely independent, only some of the special symmetries are autonomous. These results offer a novel method for deriving n-wave solutions of the pmKdV equation. Using this method, some special exact solutions of the pmKdV equation, such as the soliton, complexiton, breather and double-pole solutions, are presented.
This paper introduces a novel analytical technique called the “Variable Coefficient Second Degree Generalized Abel equation Method” (VCSDGAE), designed to tackle the complex Ginzburg–Landau equation. Unlike conventional methods that depend on constant coefficient ordinary differential equations (ODEs) and auxiliary ODEs, our approach employs variable coefficient ODEs within a sub-equation framework. We demonstrate the versatility of this method by successfully applying it to the complex Ginzburg–Landau equation. Through the presentation of analytical solutions, we showcase the method's effectiveness and efficiency, positioning it as a valuable resource for addressing complex nonlinear partial differential equations in fields such as fluid dynamics and wave propagation. The stability of the obtained soliton solutions is established through a linear stability analysis, confirming their robustness against small perturbations. This research not only broadens the spectrum of available analytical techniques but also contributes significantly to the advancement of solutions for various mathematical physics models.
We investigate the impact of the correlation between error gates on the fault-tolerant threshold in quantum circuits under three typical noise models. In the fault-tolerant encoding schemes for two fundamental quantum logical operations, we extend the conventional error injection method by simultaneously applying error gates to both control and target qubits after two-qubit gate operations, with a quantitative characterization of the correlation strength between these error gates. The results show that the fault-tolerant error threshold can be noticeably enhanced by the presence of correlations between error gates, resulting in more robust quantum circuit implementations. We further apply fault-tolerant encoding to the single-qubit teleportation circuit and investigate the effect of correlated noise on its error threshold. The results show that the threshold varies non-monotonically with the correlation strength and that the system's fault-tolerance differs significantly across noise models.
The monogamy and polygamy relations characterize the distributions of quantum entanglement in multipartite systems. We investigate the monogamy relations related to the Rényi-α entanglement (RαE) and polygamy relations related to the RαE of assistance (RαEoA). We present new entanglement monogamy relations satisfied by the η-th (η ≥ 2) power of RαE for α ≥ 2, and by the γ-th (γ ≥ 4) power of RαE for $\frac{\sqrt{7}-1}{2}\,\leqslant \,\alpha \lt 2$, respectively. Moreover, we present polygamy relations satisfied by the tth power of RαEoA with $\frac{\sqrt{7}-1}{2}\,\leqslant \,\alpha \lt \frac{\sqrt{13}-1}{2}$ for 0 ≤ t ≤ 1. We also give relationships among the residual entanglements of RαE and RαEoA, and the three tangle based on our general monogamy relations.
We consider the constraints of the purely leptonic decays of charged pseudoscalar mesons P (being π±, K±, ${D}_{(s)}^{\pm }$or B±) and the gauge boson W, P → ℓνℓ, $P\to {\ell }{\nu }_{{\ell }}\nu \bar{\nu }$, P → ℓνℓe+e− and W → ℓνℓ, on the leptophilic axion-like particles (ℓALPs, denoted as a) with masses in the range 10–100 MeV via the decays P → ℓνℓa and W → ℓνℓa, where a is assumed to escape the detector as missing energy or to decay into a pair of charged leptons. Comparing our numerical results with the latest experimental data, we find that some of these decay processes for P being π± and K± can give meaningful constraints on the flavor-diagonal coupling parameter gℓ/fa with the ℓALP mass in the range considered in this paper. The strongest constraints come from the decay ${K}^{+}\to {\mu }^{+}{\nu }_{\mu }\nu \bar{\nu }$, which set upper limits of 7.60 × 10−2–1.03 × 10−1 GeV−1 on gℓ/fa at the 90% C.L.
In the SO(2, d) gauge theory formalism of AdS gravity established in Wang and Song (2021 Class. Quantum Grav. 38 205002), the dynamics of bulk gravity emerges from the vanishing of the boundary covariant anomaly for the SO(2, d) conservation law. In parallel with the known results on chiral anomalies, we establish the descendent structure of the holographic SO(2, d) anomaly. The corresponding anomaly characteristic class, bulk Chern–Simons like action as well as the boundary effective action are constructed systematically. The anomalous conservation law is presented both in the covariant and consistent formalisms. Due to the existence of the ruler field, not only the Bardeen–Zumino polynomial, but also the covariant and consistent currents are explicitly constructed.
In this paper, we study the phenomenology of a Dirac dark matter (DM) in the Lμ − Lτ model and investigate the neutrino oscillation behavior in the dark halo. Since DM couples to muon neutrino and tau neutrino with opposite sign couplings, it contributes effective potentials, ±Aχ, to the evolution equation of the neutrino flavor transition amplitude, which can be significant for high energy neutrino oscillations in a dense DM environment. We discuss neutrino masses, lepton mixing angles, Dirac CP phase, and neutrino oscillation probabilities in the dark halo using full numerical calculations. Results show that neutrinos can endure very different matter effects. When the potential Aχ becomes ultra-large, three neutrino flavors decouple from each other.
The universal phase iD+2 of the Euclidean de Sitter path integral obstructs a straightforward state-counting interpretation of the Gibbons–Hawking entropy. Building on Maldacena's proposal that specific black-hole observers can reorganize this phase, we derive a general constraint on when such 'real observers' can succeed. By distinguishing gravitational observers from topological spectators, we show that any sector whose infrared effective action is metric independent at the de Sitter saddle factorizes in the path integral, ${Z}_{\rm{tot}\,}={Z}_{\,\rm{grav}}^{(\,\rm{obs}\,)}{Z}_{\,\rm{top}\,}$, so the imaginary phase persists regardless of the sector's information-processing capabilities. Using confining SU(3) gauge theory and topological orders as examples, we demonstrate that an information-bearing clock is necessary but insufficient: only observers whose fluctuations share the negative modes of the conformal factor belong to the special class that can remove the de Sitter phase.
We provide a theoretical proposal to achieve nonreciprocal optical routers based on a spinning microcavity exciton polariton system coupled to a tapered fiber. The mechanism for routers is revealed by nonreciprocal optomechanically induced transparency, which is obtained by transmission spectra and nonreciprocal isolate rates. Due to Sagnac effects, the transmission of photon signals along clockwise and counterclockwise directions exhibits distinct characteristics at a special frequency, resulting in clockwise or counterclockwise unidirectional transmission. Therefore, in such nonreciprocal routers, the transmission direction, output frequency, and output intensity for photon signals can be precisely controlled by adjusting Sagnac effects, pump fields, and the coupling of photon, phonon, and exciton modes. Moreover, the vacuum and thermal noise of the system cannot deteriorate the router performance. Our results open new pathways for constructing nonreciprocal optical routers, which may be useful for developing quantum networks and integrated photonic circuits.
This paper investigates the nonlinear modulation and stability of weakly two-dimensional wave packets in dusty plasmas, aiming to clarify the influence of multidimensional effects on wave evolution and frequency modulation. Employing the Davey–Stewartson (DS) equation for dust acoustic wave (DAW) dynamics, we analytically derived the dispersion relation and modulational instability conditions. Furthermore, the dependence of growth rate and modulation frequency on the wave number, density ratio, and temperature ratio is quantified. It is found that shorter waves boost frequency and instability (moderate k max). Higher electron-dust density raises frequency but suppresses instability; higher ion temperature weakens instability but lifts the high-k frequency. These findings enrich the theoretical framework for nonlinear wave modulation in dusty plasmas and guide plasma experimental diagnostics and stability control.
This study examines the structural and dynamic properties of flattened tail current sheets during intervals of weak substorm activity, based on observations from the magnetospheric multiscale mission. Using the nonlinear magnetic field gradient algorithm and geometrical invariant techniques, the analysis focuses on two distinct events characterized by opposite signs of the By component. In both cases, a prominent By is observed at the neutral current sheet's center. Fast magnetic reconnection near the neutral sheet generates intense electron jets, with electron velocities significantly exceeding ion velocities, confirming electrons as the principal charge carriers. Magnetic field lines within the neutral sheet display clockwise rotation around the northward normal, forming left-handed spiral configurations. The curvature and torsion of these field lines differ notably between events: the first event (By > 0) shows maximum curvature and zero torsion at the sheet's center, while the second event (By < 0) exhibits minimal curvature and elevated torsion. The helix angle averages approximately 45° in the first event and shifts toward 90° in the second. Geometrical invariants reveal varying magnetic topologies, with flux tube-like structures dominating the first event and a combination of flux tubes and flux ropes emerging in the second. The prevalence of flux tubes in the first event suggests a weaker magnetic field transition, as flux ropes are more effective in transporting magnetic flux. These findings highlight the significance of current sheet geometry in governing reconnection dynamics.
Omnivory, where species feed across multiple trophic levels, is a widespread feature of ecological networks. A key mechanism underlying such complexity is intraguild predation (IGP), in which a top predator consumes both an intermediate predator and a shared resource. Here, we show that Shilnikov homoclinic orbits emerge in a minimal intraguild predation model, triggering a cascade of homoclinic bifurcations near a saddle-focus equilibrium that culminates in chaos. Numerical simulations and Lyapunov spectrum analysis reveal multiple coexistence modes, ranging from regular oscillations to Shilnikov homoclinic orbits and chaos. Our model quantitatively reproduces patterns observed in natural omnivore networks, providing mechanistic insights into complex population fluctuations in ecological systems.
Reaction–diffusion infectious disease models are widely used to describe the spatial distribution of infected individuals. In this study, we construct network-based reaction–diffusion models that incorporate both higher-order interactions and advection mechanisms, formulated on a triangular lattice torus network. This idealized structure is adopted to facilitate explicit derivation and linear stability analysis of the theoretical conditions for Turing instability—analyses that would be considerably more challenging in complex heterogeneous geometries. To address the computational challenge of generating higher-order node Laplacian matrices in large-scale networks, we develop a dimensionality reduction strategy using graph-structured edge Laplacians. The theoretical analysis reveals how higher-order interactions and advection jointly influence the onset of Turing patterns. Furthermore, model fitting to real epidemic data—using a mobility network constructed from 2020 inter-prefectural commuting flows across Japan's 47 prefectures—shows that incorporating higher-order interactions results in better fitting performance compared to conventional models.
We develop a perturbative framework to calculate the mean-squared displacement (MSD) of active Brownian particles with a finite moment of inertia. Starting from the corresponding Fokker–Planck equation, we employ a Fourier transform for the spatial coordinates and Hermite polynomials as eigenfunctions for the angular velocity, which enables a systematic perturbative expansion of the MSD order by order. By resumming the resulting series in Laplace space and performing the inverse transform, we obtain an explicit expression for the MSD as a function of the moment of inertia. The analytical results are further validated by comparison with numerical simulations.
In previous studies of relativistic thermodynamics, the temperature of a static system, as perceived by a moving observer, has traditionally been treated as a scalar. This assumption has also been extended to research on the cosmic microwave background. However, the validity of this assumption is a consequence of the massless nature of photons. More generally, when an observer is in relative motion to a system, the thermal equilibrium state is characterized by a inverse temperature four-vector. In this article, we study the non-interacting massive bosonic and fermionic field systems. We derive the Lorentz transformation of the energy spectral density in the equilibrium state of these fields. In the massless limit for bosonic field, our results recover the transformation of black body radiation [G. W. Ford and R. F. O'Connell, Phys. Rev. E, 88, 044101 (2013)], which corresponds to a scalar temperature with dipole anisotropy. For the massive fields, the moving equilibrium state cannot be characterized by a corresponding scalar temperature. This result shows the necessity of introducing inverse temperature four-vector in relativistic thermodynamics.
We show the Stark effect of electronic spin in the cavity-QED system of a trapped electron on liquid helium. This effect is derived from strong spin-orbit coupling and the electric dipole interaction between the microwave-driving cavity field and orbital states of a trapped electron. We further show that the obtained effect can be used to implement the single photon detection of gigahertz (GHz) microwaves using the spin Ramsey interferometry.
We present a theoretical study of the low-energy physics of a quarter-hole-filled two-orbital bilayer Hubbard model motivated by transition-metal bilayer systems with strong orbital-selective interlayer hybridization. By explicitly treating the strong interlayer bonding of ${{d}}_{{{z}}^{2}}$ orbitals within a molecular orbital basis and projecting out high-energy electronic states, we derive a low-energy effective Kugel–Khomskii Hamiltonian describing the interplay between electron spin and emergent layer pseudospin degrees of freedom. We map out a rich ground state phase diagram featuring diverse spin and charge ordered states. These include conventional ferromagnetic and antiferromagnetic phases with layer staggered charge densities, a layer-coherent phase characterized by spontaneous interlayer quantum coherence, and a novel maximally spin-layer-entangled phase with a hidden composite spin-layer order. We show that this exotic hidden ordered phase arises from the spontaneous breaking of an emergent O(4) symmetry down to a O(3), manifesting a unique excitation spectrum with three entangled gapless Goldstone modes. Our results uncover a geometrically driven mechanism for realizing composite entanglement in strongly correlated bilayer systems and provide a concrete theoretical framework relevant to bilayer nickelate superconductors and other multi-component correlated materials.
Cooperation, fairness, trust, and resource coordination are cornerstones of modern civilization, yet their emergence remains inadequately explained, largely due to persistent discrepancies between theoretical predictions and behavioral experiments. Part of this gap may arise from the imitation learning paradigm commonly used in prior theoretical models, which assumes individuals merely copy successful neighbors according to predetermined, fixed rules. This review examines recent advances in evolutionary game dynamics that employ reinforcement learning (RL) as an alternative paradigm. In RL, individuals learn through trial and error and introspectively refine their strategies based on environmental feedback. We begin by introducing key concepts in evolutionary game theory and the two learning paradigms, then synthesize progress in applying RL to elucidate cooperation, trust, fairness, optimal resource coordination, and ecological dynamics. Collectively, these studies indicate that RL offers a promising unified framework for understanding the diverse social and ecological phenomena observed in human and natural systems.
