Imaginarity has proven to be a valuable resource in various quantum information processing tasks. A natural question arises: can the imaginarity of quantum states be broadcast via real operations? In this work, we present explicit structures for nonreal states whose imaginarity can be broadcast and cloned. That is, for a nonreal state, its imaginarity can be cloned if and only if it is a direct sum of several maximally imaginary states under orthogonal transformation, and its imaginarity can be broadcast if and only if it is a direct sum of a real state and some nonreal qubit states which are mixtures of two orthogonal maximally imaginary states under orthogonal transformation. In particular, we show that for a nonreal pure state, its imaginarity cannot be broadcast unless it is a maximally imaginary state. Furthermore, we derive a trade-off relation on the imaginarity broadcasting of pure states in terms of the measure of irreversibility of quantum states concerning real operations and the geometric measure of imaginarity. In addition, we demonstrate that any faithful measure of imaginarity is not superadditive.

Considering the importance of higher-dimensional equations that are widely applied to real nonlinear problems, many (4 + 1)-dimensional integrable systems have been established by uplifting the dimensions of their corresponding lower-dimensional integrable equations. Recently, an integrable (4 + 1)-dimensional extension of the Boiti–Leon–Manna–Pempinelli (4DBLMP) equation has been proposed, which can also be considered as an extension of the famous Korteweg–de Vries equation that is applicable in fluids, plasma physics and so on. It is shown that new higher-dimensional variable separation solutions with several arbitrary lower-dimensional functions can also be obtained using the multilinear variable separation approach for the 4DBLMP equation. In addition, by taking advantage of the explicit expressions of the new solutions, versatile (4 + 1)-dimensional nonlinear wave excitations can be designed. As an illustration, periodic breathing lumps, multi-dromion-ring-type instantons, and hybrid waves on a doubly periodic wave background are discovered to reveal abundant nonlinear structures and dynamics in higher dimensions.

Thermalization in many-body systems, especially with strong interactions, is a central question in physics. In this work, we present a novel framework for the thermalization of interacting wave systems, distinguishing between trivial (no momentum exchange) and nontrivial interactions (significant energy redistribution). This distinction leads to a statistically equivalent model with weakened interactions. By applying this to FPUT-like models, we identify a unique double scaling of thermalization times. Crucially, our findings suggest the persistence of prethermalization in strong interactions.

We introduce a novel neural network structure called strongly constrained theory-guided neural network (SCTgNN), to investigate the behaviour of the localized solutions of the generalized nonlinear Schrödinger (NLS) equation. This equation comprises four physically significant nonlinear evolution equations, namely, the NLS, Hirota, Lakshmanan–Porsezian–Daniel and fifth-order NLS equations. The generalized NLS equation demonstrates nonlinear effects up to quintic order, indicating rich and complex dynamics in various fields of physics. By combining concepts from the physics-informed neural network and theory-guided neural network (TgNN) models, the SCTgNN aims to enhance our understanding of complex phenomena, particularly within nonlinear systems that defy conventional patterns. To begin, we employ the TgNN method to predict the behaviour of localized waves, including solitons, rogue waves and breathers, within the generalized NLS equation. We then use the SCTgNN to predict the aforementioned localized solutions and calculate the mean square errors in both the SCTgNN and TgNN in predicting these three localized solutions. Our findings reveal that both models excel in understanding complex behaviour and provide predictions across a wide variety of situations.

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.

In this work, we have investigated the rotating effect on the thermodynamic properties of a 2D quantum ring. Accordingly, we have considered the radial potential of a 2D quantum ring and solved the Schrödinger equation in the presence of the Aharonov–Bohm effect and a uniform magnetic field for the considered potential. According to the solution of the equation, we calculated the eigenvalues and eigenfunctions of the considered system. Using the calculated energy spectrum, we obtained the partition function and thermodynamic properties of the system, such as the mean energy, specific heat, entropy and free energy. Our results show that the rotating effect has a significant influence on the thermophysical properties of a 2D quantum ring. We also study other effects of the rotating term: (1) the effect of different values of rotating parameters, and (2) the effect of negative rotation on the thermodynamic properties of the system. Our results are discussed in detail.

Entanglement-breaking (EB) subspaces determine the additivity of entanglement of formation (EOF), which is a long-standing issue in quantum information. We explicitly construct the two-dimensional EB subspaces of any bipartite system, when system dimensions are equal, and we apply the subspaces to construct EB spaces of arbitrary dimensions. We also present partial construction when system dimensions are different. Then, we present the notion and properties of EB subspaces for some systems, and in particular the absolute EB subspaces. We construct some examples of absolute EB subspaces, as well as EB subspaces for some systems by using multiqubit Dicke states.

In [Phys. Rev. A 107 012427 (2023)], Baldwin and Jones prove that Uhlmann–Jozsa’s fidelity between two quantum states ρ and σ, i.e., $F(\rho ,\sigma )\,:= \,{\left({\rm{Tr}}\sqrt{\sqrt{\rho }\sigma \sqrt{\rho }}\right)}^{2}$, can be written in a simplified form as $F(\rho ,\sigma )={\left({\rm{Tr}}\sqrt{\rho \sigma }\right)}^{2}$. In this article, we give an alternative proof of this result, using a function power series expansion and the properties of the trace function. Our approach not only reinforces the validity of the simplified expression but also facilitates the exploration of novel dissimilarity functions for quantum states and more complex trace functions of density operators.

In this paper, the Drinfeld–Sokolov–Satsuma–Hirota (DSSH) system is studied by using residual symmetry and the consistent Riccati expansion (CRE) method, respectively. The residual symmetry of the DSSH system is localized to Lie point symmetry in a properly prolonged system, based on which we get a new Bäcklund transformation for this system. New symmetry reduction solutions of the DSSH system are obtained by applying the classical Lie group approach on the prolonged system. Moreover, the DSSH system proves to be CRE integrable and new interesting interaction solutions between solitons and periodic waves are generated and analyzed.

We connect magic (non-stabilizer) states, symmetric informationally complete positive operator valued measures (SIC-POVMs), and mutually unbiased bases (MUBs) in the context of group frames, and study their interplay. Magic states are quantum resources in the stabilizer formalism of quantum computation. SIC-POVMs and MUBs are fundamental structures in quantum information theory with many applications in quantum foundations, quantum state tomography, and quantum cryptography, etc. In this work, we study group frames constructed from some prominent magic states, and further investigate their applications. Our method exploits the orbit of discrete Heisenberg–Weyl group acting on an initial fiducial state. We quantify the distance of the group frames from SIC-POVMs and MUBs, respectively. As a simple corollary, we reproduce a complete family of MUBs of any prime dimensional system by introducing the concept of MUB fiducial states, analogous to the well-known SIC-POVM fiducial states. We present an intuitive and direct construction of MUB fiducial states via quantum T-gates, and demonstrate that for the qubit system, there are twelve MUB fiducial states, which coincide with the H-type magic states. We compare MUB fiducial states and SIC-POVM fiducial states from the perspective of magic resource for stabilizer quantum computation. We further pose the challenging issue of identifying all MUB fiducial states in general dimensions.

In the realm of nonlinear integrable systems, the presence of decompositions facilitates the establishment of linear superposition solutions and the derivation of novel coupled systems exhibiting nonlinear integrability. By focusing on single-component decompositions within the potential BKP hierarchy, it has been observed that specific linear superpositions of decomposition solutions remain consistent with the underlying equations. Moreover, through the implementation of multi-component decompositions within the potential BKP hierarchy, successful endeavors have been undertaken to formulate linear superposition solutions and novel coupled KdV-type systems that resist decoupling via alterations in dependent variables.

The nonlinear Schrödinger equation equation is one of the most important physical models used in optical fiber theory to explain the transmission of an optical soliton. The field of chiral soliton propagation in nuclear physics is very interesting because of its numerous applications in communications and ultra-fast signal routing systems. The (1+1)-dimensional chiral dynamical structure that describes the soliton behaviour in data transmission is dealt with in this work using a variety of in-depth analytical techniques. This work has applications in particle physics, ionised science, nuclear physics, optics, and other applied mathematical sciences. We are able to develop a variety of solutions to demonstrate the behaviour of solitary wave structures, periodic soliton solutions, chiral soliton solutions, and bell-shaped soliton solutions with the use of applied techniques. Moreover, in order to verify the scientific calculations, the stability analysis for the observed solutions of the governing model is taken into consideration. In addition, the 3-dimensional, contour, and 2-dimensional visuals are supplied for a better understanding of the behaviour of the solutions. The employed strategies are dependable, uncomplicated, and effective; yet have not been utilised with the governing model in the literature that is now accessible. The resulting outcomes have impressive applications across a large number of study areas and computational physics phenomena representing real-world scenarios. The methods applied in this model are not utilized on the given models in previous literature so we can say that these describe the novelty of the work.

As a torqued version of the lattice potential Korteweg–de Vries equation, the H1^a is an integrable nonsymmetric lattice equation with only one spacing parameter. In this paper, we present the Cauchy matrix scheme for this equation. Soliton solutions, Jordan-block solutions and soliton-Jordan-block mixed solutions are constructed by solving the determining equation set. All the obtained solutions have jumping property between constant values for fixed n and demonstrate periodic structure.

In this paper, we study the N = 2 a = 1 supersymmetric KdV equation. We construct its Darboux transformation and the associated Bäcklund transformation. Furthermore, we derive a nonlinear superposition formula, and as applications we calculate some solutions for this supersymmetric KdV equation and recover the related results for the Kersten–Krasil'shchik coupled KdV-mKdV system.

The third-harmonic generation (THG) coefficient for a spherical quantum dot system with inversely quadratic Hellmann plus inversely quadratic potential is investigated theoretically, considering the regulation of quantum size, confinement potential depth and the external environment. The numerical simulation results indicate that the THG coefficient can reach the order of 10⁻¹² m² V^–2, which strongly relies on the tunable factor, with its resonant peak experiencing a redshift or blueshift. Interestingly, the effect of temperature on the THG coefficient in terms of peak location and size is consistent with the quantum dot radius but contrasts with the hydrostatic pressure. Thus, it is crucial to focus on the influence of internal and external parameters on nonlinear optical effects, and to implement the theory in practical experiments and the manufacture of optoelectronic devices.

Active matter exhibits collective motions at various scales. Geometric confinement has been identified as an effective way to control and manipulate active fluids, with much attention given to external factors. However, the impact of the inherent properties of active particles on collective motion under confined conditions remains elusive. Here, we use a highly tunable active nematics model to study active systems under confinement, focusing on the effect of the self-driven speed of active particles. We identify three distinct states characterized by unique particle and flow fields within confined active nematic systems, among which circular rotation emerges as a collective motion involving rotational movement in both particle and flow fields. The theoretical phase diagram shows that increasing the self-driven speed of active particles significantly enhances the region of the circular rotation state and improves its stability. Our results provide insights into the formation of high quality vortices in confined active nematic systems.

This paper aims to propose a fourth-order matrix spectral problem involving four potentials and generate an associated Liouville integrable hierarchy via the zero curvature formulation. A bi-Hamiltonian formulation is furnished by applying the trace identity and a recursion operator is explicitly worked out, which exhibits the Liouville integrability of each model in the resulting hierarchy. Two specific examples, consisting of novel generalized combined nonlinear Schrödinger equations and modified Korteweg–de Vries equations, are given.

The aim of this work is to investigate anisotropic compact objects within the framework of f(G) modified theory of gravity. For our present work, we utilize Krori–Barua metrics, i.e., λ(r) = Xr² + Y and β(r) = Zr². We use some matching conditions of spherically symmetric spacetime with Bardeen's model as an exterior geometry. Further, we establish some expressions of energy density and pressure components to analyze the stellar configuration of Bardeen compact stars by assuming viable f(G) models. We examine the energy conditions for different stellar structures to verify the viability of our considered models. Moreover, we also investigate some other physical features, such as equilibrium condition, equation of state parameters, adiabatic index, stability analysis, mass function, surface redshift, and compactness factor, respectively. It is worthwhile to mention here for the current study that our stellar structure in the background of Bardeen's model is more viable and stable.

This article considers a static and spherical black hole (BH) in f(Q) gravity. f(Q) gravity is the extension of symmetric teleparallel general relativity, where both curvature and torsion are vanishing and gravity is described by nonmetricity. In this study, we investigate the possible implications of quasinormal mode (QNM) modified Hawking spectra and deflection angles generated by the model. The Wentzel–Kramers–Brillouin method is used to solve the equations of motion for massless Dirac perturbation fields and explore the impact of the nonmetricity parameter (Q₀). Based on the QNM computation, we can ensure that the BH is stable against massless Dirac perturbations and as Q₀ increases the oscillatory frequency of the mode decreases. We then discuss the weak deflection angle in the weak field limit approximation. We compute the deflection angle up to the fourth order of approximation and show how the nonmetricity parameter affects it. We find that the Q₀ parameter reduces the deflection angle.

We construct the Riemann–Hilbert problem of the Lakshmanan–Porsezian–Daniel equation with nonzero boundary conditions, and use the Laurent expansion and Taylor series expansion to obtain the exact formulas of the soliton solutions in the case of a higher-order pole and multiple higher-order poles. The dynamic behaviors of a simple pole, a second-order pole and a simple pole plus a second-order pole are demonstrated.

This article's purpose is to investigate multiple high-order pole solutions for the AB system by the Riemann–Hilbert (RH) approach. We establish the RH problem through using spectral analysis to the Lax pair. Then the RH problem can be resolved and the soliton solution's formula can be given by using the Laurent expansion method. Finally, we get special soliton solutions, including dark solitons, W-type dark solitons and multiple high-pole solutions. In addition, the W-type dark soliton solutions will occur when the spectral parameters are purely imaginary.

Variational quantum algorithms are promising methods with the greatest potential to achieve quantum advantage, widely employed in the era of noisy intermediate-scale quantum computing. This study presents an advanced variational hybrid algorithm (EVQLSE) that leverages both quantum and classical computing paradigms to address the solution of linear equation systems. Initially, an innovative loss function is proposed, drawing inspiration from the similarity measure between two quantum states. This function exhibits a substantial improvement in computational complexity when benchmarked against the variational quantum linear solver. Subsequently, a specialized parameterized quantum circuit structure is presented for small-scale linear systems, which exhibits powerful expressive capabilities. Through rigorous numerical analysis, the expressiveness of this circuit structure is quantitatively assessed using a variational quantum regression algorithm, and it obtained the best score compared to the others. Moreover, the expansion in system size is accompanied by an increase in the number of parameters, placing considerable strain on the training process for the algorithm. To address this challenge, an optimization strategy known as quantum parameter sharing is introduced, which proficiently minimizes parameter volume while adhering to exacting precision standards. Finally, EVQLSE is successfully implemented on a quantum computing platform provided by IBM for the resolution of large-scale problems characterized by a dimensionality of 2²⁰.

The main focus of this paper is to address a generalized (2+1)-dimensional Hirota bilinear equation utilizing the bilinear neural network method. The paper presents the periodic solutions through a single-layer model of [3-4-1], followed by breather, lump and their interaction solutions by using double-layer models of [3-3-2-1] and [3-3-3-1], respectively. A significant innovation introduced in this work is the computation of periodic cross-rational solutions through the design of a novel [3-(2+2)-4-1] model, where a specific hidden layer is partitioned into two segments for subsequent operations. Three-dimensional and density figures of the solutions are given alongside an analysis of the dynamics of these solutions.

Exact analytical solutions are good candidates for studying and explaining the dynamics of solitons in nonlinear systems. We further extend the region of existence of spin solitons in the nonlinearity coefficient space for the spin-1 Bose–Einstein condensate. Six types of spin soliton solutions can be obtained, and they exist in different regions. Stability analysis and numerical simulation results indicate that three types of spin solitons are stable against weak noise. The non-integrable properties of the model can induce shape oscillation and increase in speed after the collision between two spin solitons. These results further enrich the soliton family for non-integrable models and can provide theoretical references for experimental studies.

Collective quantum states, such as subradiant and superradiant states, are useful for controlling optical responses in many-body quantum systems. In this work, we study novel collective quantum phenomena in waveguide-coupled Bragg atom arrays with inhomogeneous frequencies. For atoms without free-space dissipation, collectively induced transparency is produced by destructive quantum interference between subradiant and superradiant states. In a large Bragg atom array, multi-frequency photon transparency can be obtained by considering atoms with different frequencies. Interestingly, we find collectively induced absorption (CIA) by studying the influence of free-space dissipation on photon transport. Tunable atomic frequencies nontrivially modify decay rates of subradiant states. When the decay rate of a subradiant state equals to the free-space dissipation, photon absorption can reach a limit at a certain frequency. In other words, photon absorption is enhanced with low free-space dissipation, distinct from previous photon detection schemes. We also show multi-frequency CIA by properly adjusting atomic frequencies. Our work presents a way to manipulate collective quantum states and exotic optical properties in waveguide quantum electrodynamics (QED) systems.

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.

Quantifying entanglement measures for quantum states with unknown density matrices is a challenging task. Machine learning offers a new perspective to address this problem. By training machine learning models using experimentally measurable data, we can predict the target entanglement measures. In this study, we compare various machine learning models and find that the linear regression and stack models perform better than others. We investigate the model's impact on quantum states across different dimensions and find that higher-dimensional quantum states yield better results. Additionally, we investigate which measurable data has better predictive power for target entanglement measures. Using correlation analysis and principal component analysis, we demonstrate that quantum moments exhibit a stronger correlation with coherent information among these data features.

By means of the multilinear variable separation (MLVS) approach, new interaction solutions with low-dimensional arbitrary functions of the (2+1)-dimensional Nizhnik–Novikov–Veselov-type system are constructed. Four-dromion structure, ring-parabolic soliton structure and corresponding fusion phenomena for the physical quantity ${U}=\lambda {(\mathrm{ln}f)}_{{xy}}$ are revealed for the first time. This MLVS approach can also be used to deal with the (2+1)-dimensional Sasa–Satsuma system.

In this paper, the physics informed neural network (PINN) deep learning method is applied to solve two-dimensional nonlocal equations, including the partial reverse space y-nonlocal Mel'nikov equation, the partial reverse space-time nonlocal Mel'nikov equation and the nonlocal two-dimensional nonlinear Schrödinger (NLS) equation. By the PINN method, we successfully derive a data-driven two soliton solution, lump solution and rogue wave solution. Numerical simulation results indicate that the error range between the data-driven solution and the exact solution is relatively small, which verifies the effectiveness of the PINN deep learning method for solving high dimensional nonlocal equations. Moreover, the parameter discovery of the partial reverse space-time nonlocal Mel'nikov equation is analysed in terms of its soliton solution for the first time.

We present a lattice quantum chromodynamics (QCD) simulation with 2 + 1 + 1 flavor full QCD ensembles using near-physical quark masses and different spatial sizes L, at a ∼ 0.055 fm. The results show that the scalar and pesudoscalar 2-point correlator with a valence pion mass of approximately 230 MeV become degenerated at L ≤ 1.0 fm, and such an observation suggests that the spontaneous chiral symmetry breaking disappears effectively at this point. At the same time, the mass gap between the nucleon and pion masses remains larger than Λ_QCD in the entire L ∈ [0.2, 0.7] fm range.

This study introduces an innovative dual-tunable absorption film with the capability to switch between ultra-wideband and narrowband absorption. By manipulating the temperature, the film can achieve multi-band absorption within the 30–45 THz range or ultra-wideband absorption spanning 30–130 THz, with an absorption rate exceeding 0.9. Furthermore, the structural parameters of the absorption film are optimized using the particle swarm optimization (PSO) algorithm to ensure the optimal absorption response. The absorption response of the film is primarily attributed to the coupling of guided-mode resonance and local surface plasmon resonance effects. The film's symmetric structure enables polarization incoherence and allows for tuning through various means such as doping/voltage, temperature and structural parameters. In the case of a multi-band absorption response, the film exhibits good sensitivity to refractive index changes in multiple absorption modes. Additionally, the absorption spectrum of the film remains effective even at large incidence angles, making it highly promising for applications in fields such as biosensing and infrared stealth.

A quantum network concerns several independent entangled resources and can create strong quantum correlations by performing joint measurements on some observers. In this paper, we discuss an n-partite chain network with each of two neighboring observers sharing an arbitrary Bell state and all intermediate observers performing some positive-operator-valued measurements with parameter λ. The expressions of all post-measurement states between any two observers are obtained, and their quantifications of Bell nonlocality, Einstein–Podolsky–Rosen steering and entanglement with different ranges of λ are respectively detected and analyzed.

Higher dimensional entangled states demonstrate significant advantages in quantum information processing tasks. The Schmidt number is a quantity of the entanglement dimension of a bipartite state. Here we build families of k-positive maps from the symmetric information complete positive operator-valued measurements and mutually unbiased bases, and we also present the Schmidt number witnesses, correspondingly. At last, based on the witnesses obtained from mutually unbiased bases, we show the distance between a bipartite state and the set of states with a Schmidt number less than k.

The current investigation examines the fractional forced Korteweg–de Vries (FF-KdV) equation, a critically significant evolution equation in various nonlinear branches of science. The equation in question and other associated equations are widely acknowledged for their broad applicability and potential for simulating a wide range of nonlinear phenomena in fluid physics, plasma physics, and various scientific domains. Consequently, the main goal of this study is to use the Yang homotopy perturbation method and the Yang transform decomposition method, along with the Caputo operator for analyzing the FF-KdV equation. The derived approximations are numerically examined and discussed. Our study will show that the two suggested methods are helpful, easy to use, and essential for looking at different nonlinear models that affect complex processes.

In this paper, we investigate the Cauchy problem of the Sasa–Satsuma (SS) equation with initial data belonging to the Schwartz space. The SS equation is one of the integrable higher-order extensions of the nonlinear Schrödinger equation and admits a 3 × 3 Lax representation. With the aid of the $\overline{\partial }$-nonlinear steepest descent method of the mixed $\bar{\partial }$-Riemann–Hilbert problem, we give the soliton resolution and long-time asymptotics for the Cauchy problem of the SS equation with the existence of second-order discrete spectra in the space-time solitonic regions.

The axion-like particle (ALP) is one kind of the best-motivated new particles. We consider its production from the pseudoscalar mesonic decays $M\to M^{\prime} a$, with M being a pseudoscalar meson B or K. The upper limits on the flavor-conserving ALP–quark coupling parameter g_u are obtained by assuming the ALP to be an invisible particle. We find that the most severe constraint on g_u comes from the decay ${K}^{+}\to {\pi }^{+}\nu \bar{\nu }$ for 0.05 GeV ≤ M_a ≤ 0.35 GeV, while the decays ${B}^{+,0}\to {K}^{+,0}\nu \bar{\nu }$ and ${B}^{+,0}\to {\pi }^{+,0}\nu \bar{\nu }$ can also generate significant constraints.

In this paper, we study tidal forces in the Schwarzschild black hole, whose metric explicitly includes a generalized uncertainty principle (GUP) effect. We also investigate interesting features of the geodesic equations and tidal effects that are dependent on the GUP parameter α related to a minimum length. Then, by solving the geodesic deviation equations explicitly with appropriate boundary conditions, we show that α in the effective metric affects both the radial and angular components of the geodesic equation, particularly near the singularities.

Recently, a dual relation T₀(n + 1) = T_HP(n) between the minimum temperature (T₀(n + 1)) black hole phase and the Hawking–Page transition (T_HP(n)) black hole phase in two successive dimensions was introduced by Wei et al (2020 Phys. Rev. D 102 10411); this was reminiscent of the anti-de Sitter/conformal field theory (AdS/CFT) correspondence, as the Hawking–Page transition temperature could be treated as the temperature of the dual physical quantity on the boundary and the latter corresponds to that in the bulk. In this paper, we discuss the Hawking–Page transition and the dual relations in AdS black holes surrounded by dark energy in general dimensions. Our findings reveal the occurrence of the Hawking–Page transition between the thermal AdS radiation and thermodynamically stable large AdS black holes, in both the spacetime surrounded by phantom dark energy and the spacetime surrounded by quintessence dark energy. We discuss the effects of the phantom dark energy and quintessence dark energy on the Hawking–Page transition temperature. For the dual relation in particular, it works well for the case of an AdS black holes surrounded by phantom dark energy. For the case of an AdS black hole surrounded by quintessence dark energy, the dual relation should be modified under an open assumption that the state parameter and the density parameter of the quintessence dark energy depend on the dimensions of the spacetime.

The reason for the present accelerated expansion of the Universe stands as one of the most profound questions in the realm of science, with deep connections to both cosmology and fundamental physics. From a cosmological point of view, physical models aimed at elucidating the observed expansion can be categorized into two major classes: dark energy and modified gravity. We review various major approaches that employ a single scalar field to account for the accelerating phase of our present Universe. Dynamic system analysis was employed in several important models to find cosmological solutions that exhibit an accelerating phase as an attractor. For scalar field models of dark energy, we consistently focused on addressing challenges related to the fine-tuning and coincidence problems in cosmology, as well as exploring potential solutions to them. For scalar–tensor theories and their generalizations, we emphasize the importance of constraints on theoretical parameters to ensure overall consistency with experimental tests. Models or theories that could potentially explain the Hubble tension are also emphasized throughout this review.

This study analyzes the scattering of electromagnetic waves in a cold and uniform plasma-filled waveguide driven by an intense relativistic plasma beam under a strong magnetic field. The strong interaction of plasma with electromagnetic waves enables its potential use in different types of waveguides. The Helmholtz equation governs the boundary value problem, which is solved by incorporating the mode matching technique. Invoking the boundary and matching conditions and the derived orthogonality and dispersion relations in this scheme gives an exact solution to the scattering problem. The numerical results shed light on the occurrence of reflection and transmission and flow of power. The power flux is plotted against angular frequency and various duct configurations. The solution is completely validated through the benefit of analytical and numerical results. The investigation of this structure reveals not only its mathematical, but also its physical features.