Renormalization group analysis has been proposed to eliminate secular terms in perturbation solutions of differential equations and thus expand the domain of their validity. Here we extend the method to treat periodic orbits or limit cycles. Interesting normal forms could be derived through a generalization of the concept ’resonance’, which offers nontrivial analytic approximations. Compared with traditional techniques such as multi-scale methods, the current scheme proceeds in a very straightforward and simple way, delivering not only the period and the amplitude but also the transient path to limit cycles. The method is demonstrated with several examples including the Duffing oscillator, van der Pol equation and Lorenz equation. The obtained solutions match well with numerical results and with those derived by traditional analytic methods.

This is a writeup of lectures delivered at the Asian Pacific Introductory School on Superstring and Related Topics in Beijing (2006) and an expanded version of these lectures given at the Third Summer School on Strings, Fields and Holography in Nanjing (2023). It aims to provide both a historical and pedagogical account of developments in finding 1/2 Bogomol'nyi-Prasad-Sommerfield (BPS) extended string solitons during the early stage of the so-called second string revolution, before which these objects were thought to be unrelated to strings. Non-supersymmetric solutions related to brane/anti brane systems or non-BPS systems are also discussed.

Introducing ${ \mathcal P }{ \mathcal T }$-symmetric generalized Scarf-II potentials into the three-coupled nonlinear Gross–Pitaevskii equations offers a new way to seek stable soliton states in quasi-one-dimensional spin-1 Bose–Einstein condensates. In scenarios where the spin-independent parameter c₀ and the spin-dependent parameter c₂ vary, we use both analytical and numerical methods to investigate the three-coupled nonlinear Gross–Pitaevskii equations with ${ \mathcal P }{ \mathcal T }$-symmetric generalized Scarf-II potentials. We obtain analytical soliton states and find that simply modulating c₂ may change the analytical soliton states from unstable to stable. Additionally, we obtain numerically stable double-hump soliton states propagating in the form of periodic oscillations, exhibiting distinct behavior in energy exchange. For further investigation, we discuss the interaction of numerical double-hump solitons with Gaussian solitons and observe the transfer of energy among the three components. These findings may contribute to a deeper understanding of solitons in Bose–Einstein condensates with ${ \mathcal P }{ \mathcal T }$-symmetric potentials and may hold significance for both theoretical understanding and experimental design in related physics experiments.

We assume exponential corrections to the entropy of 5D charged AdS black hole solutions, which are derived within the framework of Einstein–Gauss–Bonnet gravity and nonlinear electrodynamics. Additionally, we consider two distinct versions of 5D charged AdS black holes by setting the parameters q → 0 and k → 0 (where q represents the charge, and k is the non-linear parameter). We investigate these black holes in the extended phase space, where the cosmological constant is interpreted as pressure, demonstrating the first law of black hole thermodynamics. The focus extends to understanding the thermal stability or instability, as well as identifying first and second-order phase transitions. This exploration is carried out through the analysis of various thermodynamic quantities, including heat capacity at constant pressure, Gibbs free energy (GFE), Helmholtz free energy (HFE), and the trace of the Hessian matrix. In order to visualize phase transitions, identify critical points, analyze stability and provide comprehensive analysis, we have made the contour plot of the mentioned thermodynamic quantities and observed that our results are very consistent. These investigations are conducted within the context of exponentially corrected entropies, providing valuable insights into the intricate thermodynamic behavior of these 5D charged AdS black holes under different parameter limits.

In this paper, the nonlinearization of the Lax pair and the Darboux transformation method are used to construct the rogue wave on the elliptic function background in the reduced Maxwell–Bloch system, which is described by four component nonlinear evolution equations (NLEEs). On the background of the Jacobian elliptic function, we obtain the admissible eigenvalues and the corresponding non-periodic eigenfunctions of the model spectrum problem. Then, with the help of the one-fold Darboux transformation and two-fold Darboux transformation, rogue waves on a dn-periodic background and cn-periodic background are derived, respectively. Finally, the corresponding complex dynamical properties and evolutions of the four components are illustrated graphically by choosing suitable parameters.

Understanding the effects of point liquid loading on transversely isotropic poroelastic media is crucial for advancing geomechanics and biomechanics, where precise modeling of fluid-structure interactions is essential. This paper presents a comprehensive analysis of infinite transversely isotropic poroelasticity under a fluid source, based on Biot’s theory, aiming to uncover new and previously unexplored insights in the literature. We begin our study by deriving a general solution for fluid-saturated, transversely isotropic poroelastic materials in terms of harmonic functions that satisfy sixth-order homogeneous partial differential equations, using potential theory and Almansi’s theorem. Based on these general solutions and potential functions, we construct a Green’s function for a point fluid source, introducing three new harmonic functions with undetermined constants. These constants are determined by enforcing continuity and equilibrium conditions. Substituting these into the general solution yields fundamental solutions for poroelasticity that provide crucial support for a wide range of project problems. Numerical results and comparisons with existing literature are provided to illustrate physical mechanisms through contour plots. Our observations reveal that all components tend to zero in the far field and become singular at the concentrated source. Additionally, the contours exhibit rapid changes near the point fluid source but display gradual variations at a distance from it. These findings highlight the intricate behavior of the system under point liquid loading, offering valuable insights for further research and practical applications.

Deep learning combining the physics information is employed to solve the Boussinesq equation with second-order time derivative. High prediction accuracies are achieved by adding a new initial loss term in the physics-informed neural networks along with the adaptive activation function and loss-balanced coefficients. The numerical simulations are carried out with different initial and boundary conditions, in which the relative L₂-norm errors are all around 10⁻⁴. The prediction accuracies have been improved by two orders of magnitude compared to the former results in certain simulations. The dynamic behavior of solitons and their interaction are studied in the colliding and chasing processes for the Boussinesq equation. More training time is needed for the solver of the Boussinesq equation when the width of the two-soliton solutions becomes narrower with other parameters fixed.

Recently, large-scale trapped ion systems have been realized in experiments for quantum simulation and quantum computation. They are the simplest systems for dynamical stability and parametric resonance. In this model, the Mathieu equation plays the most fundamental role for us to understand the stability and instability of a single ion. In this work, we investigate the dynamics of trapped ions with the Coulomb interaction based on the Hamiltonian equation. We show that the many-body interaction will not influence the phase diagram for instability. Then, the dynamics of this model in the large damping limit will also be analytically calculated using few trapped ions. Furthermore, we find that in the presence of modulation, synchronization dynamics can be observed, showing an exchange of velocities between distant ions on the left side and on the right side of the trap. These dynamics resemble that of the exchange of velocities in Newton’s cradle for the collision of balls at the same time. These dynamics are independent of their initial conditions and the number of ions. As a unique feature of the interacting Mathieu equation, we hope this behavior, which leads to a quasi-periodic solution, can be measured in current experimental systems. Finally, we have also discussed the effect of anharmonic trapping potential, showing the desynchronization during the collision process. It is hoped that the dynamics in this many-body Mathieu equation with damping may find applications in quantum simulations. This model may also find interesting applications in dynamics systems as a pure mathematical problem, which may be beyond the results in the Floquet theorem.

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 study explores the dynamics of charged Hayward black holes, focusing on the effects of electric charge and the length factor on accretion disk characteristics. Our results show that increasing both parameters reduces the size of the event horizon and innermost stable circular orbits (ISCO) radius, with the electric charge exerting a more pronounced influence. Additionally, the length factor and electric charge can effectively replicate the spin of a Kerr black hole. Both parameters also affect the electromagnetic radiation emitted from the accretion disk, increasing the flux, temperature, and radiative efficiency. The peak radiation occurs in the soft x-ray band, with higher values of electric charge and length factor enhancing disk luminosity and shifting the peak to higher frequencies. These findings can offer valuable insights into the accretion processes around black holes and their observable signatures, particularly in x-ray astronomy.

We simulate the gravitational redshift of quantum matter waves with a long de Broglie wavelength by tracing particle beams along geodesics, when they propagate within the rotation plane of binary black holes. The angular momentum of the binary black hole causes an asymmetric gravitational redshift distribution around the two black holes. The gravitational redshift changes the frequency of quantum matter waves and their wavelength, resulting in the different interference patterns of quantum matter waves with respect to different wavelengths. The interference pattern demonstrates strong contrast intensity and spatial order with respect to different wavelengths and the rotational angle of the binary black hole. A bright semicircular arc emerges from the interference pattern to bridge the two black holes, when they rotate to certain angles, which provides a theoretical understanding on the gravitational lensing effect of quantum matter waves.

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.

We study fundamental dark-bright solitons and the interaction of vector nonlinear Schrödinger equations in both focusing and defocusing regimes. Classification of possible types of soliton solutions is given. There are two types of solitons in the defocusing case and four types of solitons in the focusing case. The number of possible variations of two-soliton solutions depends on this classification. We demonstrate that only special types of two-soliton solutions in the focusing regime can generate breathers of the scalar nonlinear Schrödinger equation. The cases of solitons with equal and unequal velocities in the superposition are considered. Numerical simulations confirm the validity of our exact solutions.

The properties of the non-trivial quantum state in an all-optical environment come mainly from the higher-order quantum electrodynamics effect, which remains one of the few unverified predictions of this theory due to its weak signal. Here, we propose a scheme specifically designed to detect this quantum vacuum, where a tightly focused pump laser interacts with an optical frequency comb (OFC) in its resonant cavity. When the OFC pulse passes through the vacuum polarized by the high-intensity pump laser, its carrier frequency and envelope change. This can be intuitively understood as the asymmetric photon acceleration induced by the ponderomotive force of the pump laser. By leveraging the exceptional ultrahigh frequency and temporal resolution of the OFC, this scheme holds the potential to improve the accuracy of quantum vacuum signal. Combining theoretical and simulation results, we discuss possible experimental conditions, and the detectable OFC signal is shown to be orders of magnitude better than the instrumental detection threshold. This shows our scheme can be verified on the forthcoming laser systems.

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.

The theoretical challenges in understanding the nature of glass and glass transition raise significant questions in statistical and condensed matter physics. As a prototypical example of complex physical systems, glasses and the vitrification process have been central research topics, consistently attracting broad scientific interest. This focus has driven extensive studies on phenomena such as aging, non-exponential relaxation, dynamic anomalies, glass-forming ability, and the mechanical response of glasses under stress. Recent advances in computational and experimental techniques have enabled rigorous testing of theoretical models, shedding new light on glass behavior. However, the intrinsic complexity of glass and the glass transition that lies in their physics, which spans multiple length and time scales, makes the system challenging to characterize. In this review, we emphasize the need to move beyond conventional approaches and propose a topological perspective as a promising alternative to address these challenges. Specifically, our findings reveal that the diversity in particle relaxation behavior is statistically linked to a global topological feature of the transient network structures formed by the particles in a given liquid. This direction offers opportunities to uncover novel phenomena that could fundamentally reshape our understanding of glassy materials.

Urban rail transit is an efficient and environmentally friendly mode of transport, which is an important means of transportation for passengers. From a holistic point of view, this paper constructs an urban rail transit interchange topology (URTIT) network based on the interchange relationships among lines. We investigate a unique influence propagation mechanism to explore the impact of applying new technologies on the passenger travel behavior of urban rail transit. We analyze the influence from three aspects: the influence range, the influence propagation path, and the influence intensity. Based on the Dijkstra algorithm, the influence propagation paths are found according to the shortest transfer time. The improved path−based gravity model is applied to measure the influence intensity. The case study on urban rail transit in Beijing, China is carried out. The influence propagation mechanism of a single line in the Beijing URTIT network is analyzed, considering that Beijing Subway Line S1 is equipped with magnetic levitation technology. We not only quantify the impact of technologies on passenger travel behavior of urban rail transit, but also perform the sensitivity analysis. To avoid randomness, the influence propagation mechanisms of all lines are explored in this paper. The research results correspond to the situation in reality, which can provide certain references for urban rail transit operation and planning.

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.

In this work, we investigate the thermodynamic variables of a harmonic oscillator in a conical geometry metric. Moreover, we introduce an external field in the form of a Wu–Yang magnetic monopole (WYMM) and an inverse square potential into the system and analyze the results. Using an analytical approach, we obtain the energy level and study the thermodynamics at finite temperature. Our findings demonstrate that thermodynamic variables, except for the specific heat and entropy, are influenced by the topological parameters, the strength of the WYMM, and the inverse square potential.

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.

This work demonstrates that once a large number of pion is condensed in a high-energy hadron collision, the gamma-ray spectrum from π⁰ decay takes on a typical broken power-law shape, which has been documented in many astronomical observations, but we have not yet recognized it. We show that this pion condensation is caused by a large number of soft gluons condensed in protons.

We analyze the steady-state characteristics of a damped harmonic oscillator (system) in the presence of a non-Markovian bath characterized by Lorentzian spectral density. Although Markovian baths presume memoryless dynamics, the introduction of complex temporal connections by a non-Markovian environment radically modifies the dynamics of the system and its steady-state behaviour. We obtain the steady-state Green’s function and correlation functions of the system using the Schwinger–Keldysh formalism. In both rotating and non-rotating wave approximation, we analyzed various emergent properties like effective temperature and distribution function. We also explore the impact of dissipation and non-Markovian bath on the quantum Zeno and anti-Zeno effects. We show that a transition between Zeno to anti-Zeno effect can be tuned by bath spectral width and the strength of dissipation.

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.

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.

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.

Relic gravitational waves (RGWs) from the early Universe carry crucial and fundamental cosmological information. Therefore, it is of extraordinary importance to investigate potential RGW signals in the data from observatories such as the LIGO-Virgo-KAGRA network. Here, focusing on typical RGWs from the inflation and the first-order phase transition (by sound waves and bubble collisions), effective and targeted deep learning neural networks are established to search for these RGW signals within the real LIGO data (O2, O3a and O3b). Through adjustment and adaptation processes, we develop suitable Convolutional Neural Networks (CNNs) to estimate the likelihood (characterized by quantitative values and distributions) that the focused RGW signals are present in the LIGO data. We find that if the constructed CNN properly estimates the parameters of the RGWs, it can determine with high accuracy (approximately 94% to 99%) whether the samples contain such RGW signals; otherwise, the likelihood provided by the CNN cannot be considered reliable. After testing a large amount of LIGO data, the findings show no evidence of RGWs from: 1) inflation, 2) sound waves, or 3) bubble collisions, as predicted by the focused theories. The results also provide upper limits of their GW spectral energy densities of h²Ω_gw ∼ 10⁻⁵, respectively for parameter boundaries within 1) [β ∈ (−1.87, −1.85) × α ∈ (0.005, 0.007)], 2) [β/H_pt ∈ (0.02, 0.16) × α ∈ (1, 10) × T_pt ∈ (5*10⁹, 10¹⁰) Gev], and 3) [β/H_pt ∈ (0.08, 0.2) × α ∈ (1, 10) × T_pt ∈ (5 * 10⁹, 8 * 10¹⁰) Gev]. In short, null results and upper limits are obtained, and the analysis suggests that our developed methods and neural networks to search for typical RGWs in the LIGO data are effective and reliable, providing a viable scheme for exploring possible RGWs from the early Universe and placing constraints on relevant cosmological theories.

The QCD axion bubbles can form due to an explicit breaking of the Peccei–Quinn symmetry in the early Universe. In this paper, we investigate the modified formation of a QCD axion bubble in the presence of an axionlike particle (ALP), considering its resonant conversion to a QCD axion. We consider a general scenario where the QCD axion mixes with ALP before the QCD phase transition. In this scenario, the energy density of the ALP can be adiabatically transferred to the QCD axion at a temperature T_R, resulting in the suppression of the cosmic background temperature T_B at which the energy density of the QCD axion equals that of the radiation. The QCD axion bubbles form when the QCD axions arise during the QCD phase transition. Finally, we briefly discuss the impact of the formation of QCD axion bubbles on the formation of primordial black holes.

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.

Using the Melnikov method, the phenomenon of thermal chaos under periodic perturbation in the extended phase space of the modified thermodynamics of Kerr-AdS black holes is investigated. On the (P, v) section in the extended phase space, it is shown that temporal chaos will appear in the unstable spinodal region when the perturbation amplitude is larger than critical value ${\delta }_{c}^{Pv}$. We find ${\delta }_{c}^{Pv}$ is monotonically decreasing with respect to the angular momentum parameter a, which implies a large a leads to chaotic behavior more easily under time-periodic thermal perturbation. Similarly, on the $({\widehat{{\rm{\Omega }}}}_{H},J)$ section, we show there exists a critical value ${\delta }_{c}^{{\rm{\Omega }}J}$ which depends on the cosmological parameter $l=\sqrt{-3/{\rm{\Lambda }}}$. When the perturbation amplitude exceeds ${\delta }_{c}^{{\rm{\Omega }}J}$, temporal chaos occurs. As l increases, chaos becomes easier. For spatial perturbation, chaos always exists irrespective of perturbation amplitude in both the (P, v) section and $({\widehat{{\rm{\Omega }}}}_{H},J)$ section.

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.

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 this paper, we investigate the effect of exceptional points (EPs) on the violation of Leggett–Garg inequality (LGI) and no-signaling-in-time (NSIT) conditions and compare the different effects between the Hamiltonian EP (HEP) and Liouvillian EP (LEP) on those violations. We consider an open system consisting of two coupled qubits and each qubit is contacted with a thermal bath at a different temperature. In the case of omitting quantum jumps, we find that the system exhibits a second-order HEP, which separates the parameter space into an overdamped regime and an underdamped regime. In this situation, the LGI and NSIT conditions can be violated in both regimes and not violated at the HEP. In the case of without omitting quantum jumps, we find that the system exhibits a third-order LEP, which also separates the parameter space into an overdamped regime and an underdamped regime. In this situation, the LGI can only be violated in the underdamped regime with large coupling strength between the qubits. Conversely, the NSIT conditions can be violated in both regimes, as well as at the LEP, except in the overdamped regime with small coupling strength between the qubits. Comparing the violations of the LGI and NSIT conditions with HEP and LEP, we find that the quantum jumps would reduce the generation of coherence, enhance the decoherence, and lead to narrower parameter regimes that the LGI and NSIT conditions can be violated. Furthermore, in both cases, the NSIT conditions can be violated in a wider parameter regime than the LGI.

To improve the decoding performance of quantum error-correcting codes in asymmetric noise channels, a neural network-based decoding algorithm for bias-tailored quantum codes is proposed. The algorithm consists of a biased noise model, a neural belief propagation decoder, a convolutional optimization layer, and a multi-objective loss function. The biased noise model simulates asymmetric error generation, providing a training dataset for decoding. The neural network, leveraging dynamic weight learning and a multi-objective loss function, mitigates error degeneracy. Additionally, the convolutional optimization layer enhances early-stage convergence efficiency. Numerical results show that for bias-tailored quantum codes, our decoder performs much better than the belief propagation (BP) with ordered statistics decoding (BP + OSD). Our decoder achieves an order of magnitude improvement in the error suppression compared to higher-order BP + OSD. Furthermore, the decoding threshold of our decoder for surface codes reaches a high threshold of 20%.

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.

The ion channel in neurons is the basic component of signal transmission in the nervous system. The ion channel has important effects on the potential of neuron release and dynamic behavior in neural networks. Ion channels control the flow of ions into and out of the cell membrane to form an ion current, which makes the excitable membrane produce special potential changes and become the basis of nerve and muscle activity. The blockage of ion channels has a significant effect on the dynamics of neurons and networks. Therefore, it is very meaningful to study the influence of ion channels on neuronal dynamics. In this work, a hybrid ion channel is designed by connecting a charge-controlled memristor (CCM) with an inductor in series, and a magnetic flux-controlled memristor (MFCM), capacitor, and nonlinear resistor are connected in parallel with the mixed ion channel to obtain the memristor neural circuit. Furthermore, the oscillator model with a hybrid ion channel and its energy function are calculated, and a map neuron is obtained by linearizing the neuron oscillator model. In addition, an adaptive regulation method is designed to explore the adaptive regulation of energy on the dynamic behaviors of the map neuron. The results show that the dynamics of a map neuron with a hybrid ion channel can be controlled by parameters and external magnetic fields. This study is also used to research synchronization between map neurons and collective behaviors in the map neurons network.

A polynomial scheme is proposed here to compute exact solutions of nonlinear partial differential equations (NPDEs) based on a series expansions of solutions and a renormalization group (RG) related resummation. The most salient feature of the current approach is that only linear algebraic equations need to be solved to implement the resummation for closed-form exact solution and parameter dependence, which does not require any sophisticated analysis like Cole–Hopf transformation or Painlevé test. New exact solutions of typical NPDEs are computed with this novel method, including one- and two-soliton (solitary wave) solutions, periodic solutions of exponential or elliptic function type. Moreover, exact reduced equations may also be conveniently computed for further analysis.

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.