Communications in Theoretical Physics

Emergence refers to the existence or formation of collective behaviors in complex systems. Here, we develop a theoretical framework based on the eigen microstate theory to analyze the emerging phenomena and dynamic evolution of complex system. In this framework, the statistical ensemble composed of M microstates of a complex system with N agents is defined by the normalized N × M matrix A, whose columns represent microstates and order of row is consist with the time. The ensemble matrix A can be decomposed as ${\boldsymbol{A}}={\sum }_{I=1}^{r}{\sigma }_{I}{{\boldsymbol{U}}}_{I}\otimes {{\boldsymbol{V}}}_{I}$, where $r={\rm{\min }}(N,M)$, eigenvalue σ_I behaves as the probability amplitude of the eigen microstate U_I so that ${\sum }_{I=1}^{r}{\sigma }_{I}^{2}=1$ and U_I evolves following V_I. In a disorder complex system, there is no dominant eigenvalue and eigen microstate. When a probability amplitude σ_I becomes finite in the thermodynamic limit, there is a condensation of the eigen microstate U_I in analogy to the Bose–Einstein condensation of Bose gases. This indicates the emergence of U_I and a phase transition in complex system. Our framework has been applied successfully to equilibrium three-dimensional Ising model, climate system and stock markets. We anticipate that our eigen microstate method can be used to study non-equilibrium complex systems with unknown order-parameters, such as phase transitions of collective motion and tipping points in climate systems and ecosystems.

Nonplanar electron acoustic waves (NEAWs) with double spectral index-distributed hot electrons are studied under the two-temperature electrons model in a collisionless unmagnetized plasma. Using this model, the Korteweg–de Vries (KdV) equation is derived in nonplanar geometry. On the basis of the solutions of KdV equation, alterations of velocity, width, and amplitude of acoustic waves having various plasma factors are investigated. Nonlinear and dispersion coefficients obtained rely on double spectral index parameters r and q, and particle density α. The combined influence of these factors significantly alters the features of electron acoustic waves in nonplanar geometry. This study is expected to contribute to the understanding of nonlinear principles that underlie nonplanar electrostatic waves in laboratory plasmas as well as in space.

A device is defined as a memristor if it exhibits a pinched hysteresis loop in the current–voltage plane, and the loop area shrinks with increasing driven frequency until it gets a single-valued curve. However, the explaination of the underlying mechanism for these fingerprints is still limited. In this paper, we propose the differential form of the memristor function, and we disclose the dynamical mechanism of the memristor according to the differential form. The symmetry of the curve is only determined by the driven signal, and the shrinking loop area results from the shrinking area enclosed by driven signal and the time coordinate axis. Significantly, we find the condition for the phase transition of a memristor, and the resistance switches between the positive resistance, local zero resistance, and local negative resistance. This phase transition is confirmed in the HP memristor. These results advance the understanding of the dynamics mechanism and phase transition of a memristor.

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.

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 this paper, an active tunable terahertz bandwidth absorber based on single-layer graphene is proposed, which consists of a graphene layer, a photo crystal plate, and a gold substrate. When the Fermi energy (E_f) of graphene is 1.5 eV, the absorber shows high absorption in the range of 3.7 THz–8 THz, and the total absorption rate is 96.8%. By exploring the absorption mechanism of the absorber, the absorber shows excellent physical regulation. The absorber also shows good adjustability by changing the E_f of graphene. This means that the absorber exhibits excellent tunability by adjusting the physical parameters and E_f of the absorber. Meanwhile, the absorber is polarization independent and insensitive to the incident angle. The fine characteristics of the absorber mean that the absorber has superior application value in many fields such as biotechnology and space exploration.

A mobile Coulomb gas permeating a fixed background crystalline lattice of charged colloidal crystals is subject to an electrostatic-elastic coupling, which we study on the continuum level by introducing a minimal coupling between electrostatic and displacement fields. We derive linearized, Debye–Hückel-like mean-field equations that can be analytically solved, incorporating the minimal coupling between electrostatic and displacement fields leading to an additional effective attractive interaction between mobile charges that depends in general on the strength of the coupling between the electrostatic and displacement fields. By analyzing the Gaussian fluctuations around the mean-field solution we also identify and quantify the region of its stability in terms of the electrostatic-elastic screening length. This detailed continuum theory incorporating the standard lattice elasticity and electrostatics of mobile charges provides a baseline to investigate the electrostatic-elastic coupling for microscopic models in colloid science and materials science.

This study investigates the dromion structure within the context of (2+1)-dimensional modulated positron-acoustic waves in a magnetoplasma consisting of inertial cold positrons and inertialess nonthermal hot electrons and positrons as well as stationary positive ions. The reductive perturbation approach reduces the fluid governing equations to the plasma model to a Davey–Stewartson system. This study provides a detailed analysis of the influence of many related plasma parameters, including the density ratio of hot and cold positrons, the external magnetic field strength, the nonthermal parameter and the density ratio of electrons and cold positrons, on the growing rate of instability. Using the Hirota Bilinear method, it is found that the system supports some exact solutions, such as one- and two-dromion solutions. The change of plasma parameters significantly enhances the characteristics of dromion solutions. The elastic and inelastic collisions between two dromions are discussed at different times. The relevance of this study can help us to understand the various types of collision between energetic particles in confined plasma during the production of energy by thermonuclear fusion.

We have developed a class of charged, anisotropic, and spherically symmetric solutions, described by the function $f({ \mathcal R },{ \mathcal A })={ \mathcal R }+\alpha { \mathcal A }$, where ${ \mathcal R }$ represents the Ricci scalar, ${ \mathcal A }$ is the anticurvature scalar, and α is the coupling constant. The model was constructed using the Karmarkar condition to obtain the radial metric component, while the time metric component followed the approach proposed by Adler. We assumed a specific charge distribution inside the star to build the model. To ensure a smooth spacetime transition, we established boundary conditions, considering Bardeen's solution for the exterior spacetime. Additionally, we examined various physical aspects, such as energy density, pressure components, pressure anisotropy, energy conditions, the equation of state, surface redshift, compactness factor, adiabatic index, sound speed, and the Tolman–Oppenheimer–Volkoff equilibrium condition. All these conditions were met, demonstrating that the solutions we obtained are physically viable.

We study the motion of an inertial microswimmer in a non-Newtonian environment with a finite memory and present the theoretical realization of an unexpected transition from random self-propulsion to rotational (circular or elliptical) motion. Further, the rotational motion of the swimmer is followed by spontaneous local directional reversal, yet with a steady-state angular diffusion. Moreover, the advent of this behaviour is observed in the oscillatory regime of the inertia-memory parameter space of the dynamics. We quantify this unconventional rotational motion of the microswimmer by measuring the time evolution of the direction of its instantaneous velocity or orientation. By solving the generalized Langevin model of non-Markovian dynamics of an inertial active Ornstein–Uhlenbeck particle, we show that the emergence of the rotational (circular or elliptical) trajectory is due to the presence of both inertial motion and memory in the environment.

The future space-borne gravitational wave (GW) detectors would provide a promising probe for the new physics beyond the standard model that admits the first-order phase transitions. The predictions for the GW background vary sensitively among different concrete particle physics models but also share a large degeneracy in the model buildings, which motivates an effective model description on the phase transition based on different patterns of the electroweak symmetry breaking (EWSB). In this paper, using the scalar N-plet model as a demonstration, we propose an effective classification for three different patterns of EWSB: (1) radiative symmetry breaking with classical scale invariance, (2) the Higgs mechanism in a generic scalar extension, and (3) higher-dimensional operators. We conclude that a strong first-order phase transition could be realized for (1) and (2) with a small quartic coupling and a small isospin of an additional N-plet field for the light scalar field model with and without the classical scale invariance, and (3) with a large mixing coupling between scalar fields and a large isospin of the N-plet field for the heavy scalar field model.

In the present study, we investigated the existence of arbitrary amplitude dust acoustic solitons by considering the Cairns distributed ions, negatively charged streaming dust grains along with (r, q) distributed electrons in an un-magnetized dusty plasma. We used the pseudopotential technique to obtain the solitary wave solution. It is seen that the coexistence of rarefactive and compressive solitons is possible when ions and electrons are nonthermally distributed. We found that the soliton characteristics are strongly dependent on the choice of velocity distribution function through the nonthermal spectral indices $r,{q}$, $\alpha$ as well as on the ion and dust temperatures. For (r, q) distributed electrons, we found that the soliton amplitude increases (decreases) with smaller (higher) values of negative (positive) $r$. For Cairns distributed ions, we found a transition from negative to positive polarity solitary structures with the coexistence in between as the nonthermal parameter $\alpha$ increases. Our results gave a better explanation for the formation of dust acoustic solitary structures and their dependence on high and low energy particles in nonthermal distribution profiles in space environments.

We obtain for the first time the analytic two-loop four-point MHV lightlike form factor of the stress-tensor supermultiplet in planar ${ \mathcal N }=4$ SYM where the momentum q carried by the operator is taken to be massless. Remarkably, we find that the two-loop result can be constrained uniquely by the infrared divergences and the collinear limits using the master-bootstrap method. Moreover, the remainder function depends only on three dual conformal invariant variables, which can be understood from a hidden dual conformal symmetry of the form factor arising in the lightlike limit of q. The symbol alphabet of the remainder contains only nine letters, which are closed under the action of the dihedral group D₄. Based on the dual description in terms of periodic Wilson lines (null-wrapped polygons), we also consider a new OPE picture for the lightlike form factors and introduce a new form factor transition that corresponds to the three-point lightlike form factor. With the form factor results up to two loops, we make some all-loop predictions using the OPE picture.

We have developed a class of charged, anisotropic, and spherically symmetric solutions, described by the function $f({ \mathcal R },{ \mathcal A })={ \mathcal R }+\alpha { \mathcal A }$, where ${ \mathcal R }$ represents the Ricci scalar, ${ \mathcal A }$ is the anticurvature scalar, and α is the coupling constant. The model was constructed using the Karmarkar condition to obtain the radial metric component, while the time metric component followed the approach proposed by Adler. We assumed a specific charge distribution inside the star to build the model. To ensure a smooth spacetime transition, we established boundary conditions, considering Bardeen's solution for the exterior spacetime. Additionally, we examined various physical aspects, such as energy density, pressure components, pressure anisotropy, energy conditions, the equation of state, surface redshift, compactness factor, adiabatic index, sound speed, and the Tolman–Oppenheimer–Volkoff equilibrium condition. All these conditions were met, demonstrating that the solutions we obtained are physically viable.

In this article, a well-known anisotropic solution, the Tolman–Finch–Skea (TFS) solution, is studied using the gravitational decoupling approach within the framework of 4D Einstein–Gauss–Bonnet (EGB) gravity. The radial metric potential is modified linearly through the minimal geometric deformation approach, while the temporal component of the metric remains unchanged. The system of EGB field equations is decomposed into two distinct sets of field equations: one corresponding to the standard energy-momentum tensor and the other associated with an external gravitational source. The first system is solved using the aforementioned known solution, while the second is closed by imposing the mimic constraint on pressure. Moreover, the junction conditions at the inner and outer surfaces of the stellar object are examined, considering the Boulware–Deser 4D space-time as the external geometry. The physical properties of the stellar model are analyzed using parameters such as energy conditions, causality conditions, compactness, and redshift.

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.

We review the theoretical aspects of holographic dark energy (HDE) in this paper. Making use of the holographic principle (HP) and the dimensional analysis, we derive the core formula of the original HDE (OHDE) model, in which the future event horizon is chosen as the characteristic length scale. Then, we describe the basic properties and the corresponding theoretical studies of the OHDE model, as well as the effect of adding dark sector interaction in the OHDE model. Moreover, we introduce all four types of HDE models that originate from HP, including (1) HDE models with the other characteristic length scale; (2) HDE models with extended Hubble scale; (3) HDE models with dark sector interaction; (4) HDE models with modified black hole entropy. Finally, we introduce the well-known Hubble tension problem, as well as the attempts to alleviate this problem under the framework of HDE. From the perspective of theory, the core formula of HDE is obtained by combining the HP and the dimensional analysis, instead of adding a DE term into the Lagrangian. Therefore, HDE remarkably differs from any other theory of DE. From the perspective of observation, HDE can fit various astronomical data well and has the potential to alleviate the Hubble tension problem. These features make HDE a very competitive dark energy scenario.

In this paper, we present an overview on recent progress in studies of QCD at finite temperature and densities within the functional renormalization group (fRG) approach. The fRG is a nonperturbative continuum field approach, in which quantum, thermal and density fluctuations are integrated successively with the evolution of the renormalization group (RG) scale. The fRG results for the QCD phase structure and the location of the critical end point (CEP), the QCD equation of state (EoS), the magnetic EoS, baryon number fluctuations confronted with recent experimental measurements, various critical exponents, spectral functions in the critical region, the dynamical critical exponent, etc, are presented. Recent estimates of the location of the CEP from first-principle QCD calculations within fRG and Dyson–Schwinger equations, which pass through lattice benchmark tests at small baryon chemical potentials, converge in a rather small region at baryon chemical potentials of about 600 MeV. A region of inhomogeneous instability indicated by a negative wave function renormalization is found with μ_B ≳ 420 MeV. It is found that the non-monotonic dependence of the kurtosis of the net-proton number distributions on the beam collision energy observed in experiments could arise from the increasingly sharp crossover in the regime of low collision energy.

Ab initio approaches are among the most advanced models to solve the nuclear many-body problem. In particular, the no-core–shell model and many-body perturbation theory have been recently extended to the Gamow shell model framework, where the harmonic oscillator basis is replaced by a basis bearing bound, resonance and scattering states, i.e. the Berggren basis. As continuum coupling is included at basis level and as configuration mixing takes care of inter-nucleon correlations, halo and resonance nuclei can be properly described with the Gamow shell model. The development of the no-core Gamow shell model and the introduction of the $\hat{\bar{Q}}$-box method in the Gamow shell model, as well as their first ab initio applications, will be reviewed in this paper. Peculiarities compared to models using harmonic oscillator bases will be shortly described. The current power and limitations of ab initio Gamow shell model will also be discussed, as well as its potential for future applications.

In recent several years, the tensor force, one of the most important components of the nucleon–nucleon force, has been implemented in time-dependent density functional theories and it has been found to influence many aspects of low-energy heavy-ion reactions, such as dissipation dynamics, sub-barrier fusions, and low-lying vibration states of colliding partners. Especially, the effects of tensor force on fusion reactions have been investigated from the internuclear potential to fusion crosssections systematically. In this work, we present a mini review on the recent progress on this topic. Considering the recent progress of low-energy reaction theories, we will also mention more possible effects of the tensor force on reaction dynamics.

Theoretical challenges in understanding the nature of glass and the glass transition remain significant open 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 glassy 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.

The Richtmyer-Meshkov (RM) instability plays an important role in various natural and engineering fields, such as inertial confinement fusion. In this work, the effect of relaxation time on the RM instability under reshock impact is investigated by using a two-component discrete Boltzmann method. The hydrodynamic and thermodynamic characteristics of the fluid system are comprehensively analyzed from the perspectives of the density gradient, vorticity, kinetic energy, mixing degree, mixing width, and non-equilibrium intensity. Simulation results indicate that for larger relaxation time, the diffusion and dissipation are enhanced, the physical gradients decrease, and the growth of the interface is suppressed. Furthermore, the non-equilibrium manifestations show complex patterns, driven by the competitive physical mechanisms of the diffusion, dissipation, shock wave, rarefaction wave, transverse wave, and fluid instabilities. These findings provide valuable insights into the fundamental mechanism of compressible fluid flows.

This work revisits the analysis of charged Casimir wormhole solutions within the framework of Einstein-Gauss-Bonnet (EGB) gravity, addressing a critical inconsistency in the approach presented by Farooq et al. Specifically, we show that their use of four-dimensional Casimir and electric field energy densities is incompatible with the higher-dimensional nature of EGB gravity, which requires D ≥ 5. We provide the correct formulation for the energy densities and revise the wormhole properties under this framework, offering a refined perspective on the interplay between extra dimensions and Casimir effects in EGB gravity.

This paper presents a tunable and polarimetric-insensitive wideband metamaterial absorber based on single layer graphene. By comparing simulated experimental data with theoretical derivation, it was found that the absorbance of the material can be sustained above 90% in the frequency range of 2.78 to 7.14 (4.36) THz, of which the absorption rate exceeds 99% in the frequency range of 4.1-4.54 (0.44) THz, and remarkably, perfect absorption is achieved at 4.32 THz. In the range of 2.78-7.14 THz, the average absorption rate is 96.1%, By adjusting the physical size of the graphene layer pattern, we can change the working band gap of the absorber. By applying a voltage to modulate the Fermi level of graphene, we can increase the absorption bandwidth. When the chemical potential is 1.0 eV, at a bandwidth of 4.36 THz, its absorption rate exceeds 90%. The working principle of absorbing materials was deeply explored using the principles of electromagnetic field distribution and impedance adaptation. Through detailed analysis of different polarization states and incident angles, we found that the absorber is not sensitive to polarization due to its symmetrical structure, and found that it exhibits low sensitivity at incidence angles. In addition, after comparative analysis, significant differences were observed in the absorption efficiency of the absorber under various relaxation time conditions, and the obtained data were elaborated in detail using the carrier mechanism of plasma vibration. We found that in addition to obtaining an almost perfect absorber with wide band by adjusting the parameters, it is also feasible to obtain an approximately narrow band absorber by changing the relaxation time without having to re-manufacture the structure. The absorber offers several advantages, including tunable, wide absorption band, high absorption rate, polarization insensitivity, simple structure, etc. Therefore, this absorber exhibits great potential for absorption and sensing in the terahertz band.

Abstract
Intracellular transports of cargoes are performed by biological molecular motors that move processively along their linear tracks. In some cases, the cargo can interact with the track. A typical example of these cases is the transport of a major mitotic signaling module, the chromosomal passenger complex (CPC), along the microtubule toward the equatorial cortex by a kinesin-6 motor during anaphase, where the CPC can interact with the microtubule. Here, an analytical theory is presented on the dynamics of the molecular motor transporting a track-interacted cargo. The theory is then applied to the transports of the track-interacted cargo by kinesin-6 and by kinesin-1 motors, with the theoretical results reproducing quantitatively the available experimental data. It is found that a diffusive cargo along the track, with the diffusion constant ≥ 0.1 μm²/s, can enhance largely the processivity relative to the non-diffusive cargo and relative to the cargo having no interaction with the track.
Keywords: molecular motor; intracellular cargo transport; kinesin