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.

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.

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.

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.

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.

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 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.

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 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.

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.

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.

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.

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.

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.

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.

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.

In this paper, we investigate the (2+1)-dimensional three-component long-wave-short-wave resonance interaction system, which describes complex systems and nonlinear wave phenomena in physics. By employing the Hirota bilinear method, we derive the general nondegenerate N-soliton solution of the system, where each short-wave component contains N arbitrary functions of the independent variable y. The presence of these arbitrary functions in the analytical solution enables the construction of a wide range of nondegenerate soliton types. Finally, we illustrate the structural features of several novel nondegenerate solitons, including M-shaped, multiple double-hump, and sawtooth double-striped solitons, as well as interactions between nondegenerate solitons, such as dromion-like solitons and solitoffs, with the aid of figures.

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.

We investigate phase estimation in a lossy interferometer using entangled coherent states, with a particular focus on a scenario where no reference beam is employed. By calculating the quantum Fisher information, we reveal two key results: (1) the metrological equivalence between scenarios with and without a reference beam, established under ideal lossless conditions for the two-phase-shifting configuration, breaks down in the presence of photon loss, and (2) the pronounced inferior performance of ECSs relative to NOON states, observed in the presence of a reference beam, disappears in its absence.

The Josephson junction is typically tuned by a magnetic field or electrostatic gate to realize a superconducting (SC) transistor, which manipulates the supercurrent in integrated SC circuits. Here, we propose a theoretical scheme for a light-controlled SC transistor, which is composed of two superconductor leads weakly linked by a coherent light-driven quantum dot. We discover a Josephson-like relation for the supercurrent ${I}_{{\rm{s}}}={I}_{c}({\rm{\Phi }})\,\sin {\rm{\Phi }}$, where both the supercurrent phase Φ and magnitude I_c can be completely controlled by the phase, intensity, and detuning of the driving light. Additionally, the supercurrent magnitude displays a Fano profile with the increase of the driving light intensity, which is understood by comparing the level splitting of the quantum dot under light driving with the SC gap. Moreover, when two such SC transistors form a loop, they constitute a light-controlled SC quantum interference device (SQUID). Such a light-controlled SQUID can demonstrate the Josephson diode effect, and the optimized non-reciprocal efficiency achieves up to 54%, surpassing the maximum record reported in recent literature. Thus, our scheme delivers a promising platform for performing diverse and flexible manipulations in SC circuits.

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.

In this paper, the decoherence dynamics and spectral response of an optomechanical system, with linear and quadratic couplings, is addressed. The decoherence considered arises from pure dephasing, described by the Milburn stochastic evolution of the Schrödinger equation. In the first part of this paper, it is shown how the decoherence rate influences the evolution of the number of phonons, and the quadrature of the mechanical resonator. In the second part of the paper, an attempt to look at the spectral response of the mechanical part of the system is given using non-stationary spectroscopy. The response of the resonator in its equilibrium position is emphasized when the single-photon regime is considered. Coherent states in the cavity field and the mechanical resonator are also represented. Results and discussion comparing the inclusions of the linear, quadratic, and linear-quadratic couplings are given, regarding the influence of the dephasing in the decoherence mechanism.

We consider the recently developed black hole in massive Einstein-dilaton gravity including the coupling of the dilaton scalar field to massive graviton terms. This model has different horizon structures such as event horizons and inner horizons depending on the values of certain parameters. These variations influence how the black hole interacts with its surroundings. We utilize the well-known Novikov–Thorne model to investigate the thin accretion disks into this interesting model. Our research shows a crucial correlation between the dynamics of the accretion disk and the parameters of dilatonic black holes in dilaton-massive gravity. We observe that dilaton-massive gravity leads to significant contraction and outward expansion. We offer a detailed analysis of accretion by examining both direct and secondary images at various radial distances and observation angles.

Verlinde's emergent gravity (VEG) posits that gravity arises as an emergent phenomenon rooted in the entropic properties of spacetime, challenging the traditional view of gravity as a fundamental force. Building on this paradigm, recent developments have introduced a novel class of black holes within the VEG framework, revealing intriguing connections between apparent dark matter effects and the distribution of baryonic matter. In this study, we delve into the observational signatures of a Simpson–Visser (SV) Minkowski core regular black hole in VEG, focusing on its shadow images and intensity profiles. Our analysis highlights the profound influence of model parameters, including A (governing baryonic matter distribution), B (strength of interaction between apparent dark matter and baryonic matter), and n (characterizing diverse spacetime geometries), on the effective potential and observable properties. Notably, we find that the modifications introduced by these parameters lead to distinct changes in the black hole's shadow size and intensity distribution. Comparing our results to the Reissner–Nordström (RN) black hole, we uncover a striking reduction in the apparent shadow size and an enhancement in intensity for the SV solution in VEG.

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.

In this work, we mainly study Bell nonlocality and quantum steerability of two-coupled double quantum dots (DQDs) system via local filtering operation. We compare and analyze the influence of the Coulomb potential, temperature, tunneling parameter and local filtering operation on quantum steering and Bell nonlocality in the system. The results show that quantum steering and nonlocality first increase and then decrease but never vanish even for the stronger value of the Coulomb potential. Quantum steering and Bell nonlocality would degrade with the increase of temperature. The filtering process does not increase the degree of steerability, but decreases the range of quantum steerability. In addition, it is noteworthy that a peculiar phenomenon exists: the Einstein–Podolsky–Rosen (EPR) steering asymmetry between Alice and Bob first increase, then decrease to zero and finally increases as the tunneling strength increases. However, this phenomenon does not appear with no operation between Alice and Bob.

In this paper, we study the problem of sampling complexity for channel discrimination with respect to two different strategies: product strategy and adaptive strategy. We first formally introduce the definitions of the sampling complexity of the channels under the framework of hypothesis testing , wherein the goal is to determine the minimum number of samples needed to reach a desired error probability. We then establish the lower and upper bounds on the sampling complexity of the symmetric, asymmetric, and error exponent hypothesis testing settings. We show that, by imposing product strategy on testing, the bounds are always characterized by the generalized channel divergence, while with adaptive strategy, the bounds are characterized by the amortized channel divergence. Finally, we analyze two concrete examples, and obtain that the adaptive strategy can not lead to an advantage to the problem of determining the sampling complexity for classical-quantum channels, which can bring advantages for generalized amplitude damping channels.

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.

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.

Nonclassical light fields exhibit unique quantum characteristics that not only expand the scope of optical research but also provide a solid foundation for advancements in quantum technologies. In this study, we investigate a system consisting of one-¹³³Cs atom placed in a resonant cavity. Pumped by 459 nm laser light, the system generates cavity modes corresponding to the atomic 7S_1/2 → 6P_3/2 (1470 nm) and 7S_1/2 → 6P_1/2 (1359 nm) transitions, which are associated with the clock states of the cesium active optical clock. By analyzing the statistical and dynamical properties of the fields, we systematically explore the nonclassical behavior of the system under varying coupling strengths and cavity decay rates. We identify parameter regions where both individual fields and their cross-correlation exhibit nonclassicality, with the Cauchy–Schwarz (CS) violation coefficient R reaching a maximum of 13.9. This demonstrates the system’s ability to generate highly nonclassical photon pairs, enriching the repertoire of nonclassical light sources.

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.

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.

This study investigates the key characteristics of compact star configurations within the framework of Rastall’s theory of gravity, employing the Krori–Barua ansatz. By forming the field equations for a spherically symmetric line element with an isotropic matter source through Krori–Barua metric potentials, we derive the modified Tolman–Oppenheimer–Volkov equation. This equation is crucial for studying the mass–radius function, the compactness factor, and the surface redshift. Additionally, we examine various physical aspects, including energy density, pressure evolution, equation of state, adiabatic index, and stability analysis, to assess the model’s viability. Rastall’s theory, which extends general relativity by relaxing the conservation of energy and momentum, plays a central role in our analysis, particularly in understanding the enhanced stability of compact stars. Our results provide strong evidence that within Rastall’s gravitational framework, the proposed stellar structures exhibit significant stability, suggesting that this theory may offer new perspectives on the behavior of such stars.

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.

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.

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.

In this paper, we propose a perfect entanglement swapping protocol for generating a shared three-qubit W state between two remote parties in a deterministic manner. Our method offers a reliable alternative to existing probabilistic protocols for W state entanglement swapping, which is crucial for various quantum information processing tasks. We present a detailed quantum circuit design, implemented using the Qiskit simulator, that outlines the preparation of W states and the execution of joint measurements required for the entanglement swapping process. Furthermore, we analyze the effects of imperfect operations and noisy communication channels on the fidelity of the resulting shared W state. To address these challenges, we introduce a weak measurement-based purification method that enhances fidelity in the presence of amplitude damping. Through mathematical analysis and Qiskit simulations, we demonstrate the effectiveness of our proposed protocol, offering a practical solution for high-fidelity W state generation in real-world quantum communication scenarios.

In this article, a Generalized Calogero–Bogoyavlenskii–Schiff (CBS) equation is studied, serving as an extended shallow water wave model in higher dimensions. Firstly, utilizing the Bell polynomial method, the bilinear form of the equation, bilinear Bäcklund transformation, Lax pair and infinite conservation laws are derived, confirming the equation’s complete integrability in the context of the Lax pair. Subsequently, the nonlinear superposition formula of the equation is constructed based on the derived bilinear Bäcklund transformation and an array of infinite superposition soliton solutions of the equation are formulated using this nonlinear superposition formula. Lastly, leveraging the obtained bilinear equation, infinite superposition solutions of various functional types are constructed. Their dynamic characteristics are analyzed through illustrated solution images. It is noteworthy that this paper not only uncovers a multitude of properties through the Bell polynomial method but also derives both infinite linear and nonlinear superposition solutions, enriching the diversity of solutions, these aspects have not been previously explored in existing literature.