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.

In the paper we derive new solutions for the discrete and continuous Schwarzian Korteweg-de Vries (SKdV) equations. These solutions are characterized by trigonometric functions as backgrounds. For the discrete SKdV equation, its solutions are derived by using trigonometric function seeds and Bäcklund transformation. Solutions for the continuous SKdV equation are obtained by taking continuum limits.

The nonisospectral effect λ_t=α(t)λ satisfied by spectral parameter λ opens up a new scheme for constructing localized waves to some nonlinear partial differential equations. In this paper, we perform this effect on a complex nonisospectral nonpotential sine-Gordon equation by the bilinearization reduction method. From an integrable nonisospectral Ablowitz-Kaup-Newell-Segur equation, we construct some exact solutions in double Wronskian form to the reduced complex nonisospectral nonpotential sine-Gordon equation. These solutions, including soliton solutions, Jordan-block solutions and interaction solutions, exhibit localized structure, whose dynamics are analyzed with graphical illustration. The research ideas and methods in this paper can be generalized to other negative order nonisospectral integrable systems.

Complex numbers play a pivotal role in both mathematics and physics, particularly in quantum mechanics, and are extensively utilized to depict the behavior of microscopic particles. Recognizing the significance of complex numbers, a framework of imaginarity resource theory has recently been established. In this work, we propose two types of imaginarity monotones induced by the unified (α, β)-relative entropy and investigate their properties. Moreover, we give explicit examples to illustrate our results.

The Husimi function (Q-function) of a quantum state is the distribution function of the density operator in the coherent state representation. It is widely used in theoretical research, such as in quantum optics. The Wehrl entropy is the Shannon entropy of the Husimi function, and is non-zero even for pure states. This entropy has been extensively studied in mathematical physics. Recent research also suggests a significant connection between the Wehrl entropy and many-body quantum entanglement in spin systems. We investigate the statistical interpretation of the Husimi function and the Wehrl entropy, taking the system of N spin-1/2 particles as an example. Due to the completeness of coherent states, the Husimi function and Wehrl entropy can be explained via the positive operator-valued measurement (POVM) theory, although the coherent states are not a set of orthonormal basis. Here, with the help of the Bayes' theorem, we provide an alternative probabilistic interpretation for the Husimi function and the Wehrl entropy. This interpretation is based on direct measurements of the system, and thus does not require the introduction of an ancillary system as in the POVM theory. Moreover, under this interpretation the classical correspondences of the Husimi function and the Wehrl entropy are just phase-space probability distribution function of N classical tops, and its associated entropy, respectively. Therefore, this explanation contributes to a better understanding of the relationship between the Husimi function, Wehrl entropy, and classical-quantum correspondence. The generalization of this statistical interpretation to continuous-variable systems is also discussed.

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.

As one of the famous effects in the quantum Rabi model (QRM), Rabi oscillation may lead to the occurrence of quantum dynamical behaviors without classical dynamic counterparts, such as quantum collapse and revival effects. In this paper, we focus on studying the long-time quantum signatures of chaos in the large atom-light frequency ratios of the Rabi model. It is shown that the saturated values of the entanglement entropy for initial states located in chaotic sea are higher than that in the regular regions, and the Husimi Q function are more dispersed in phase space. Moreover, we observed that the long-time average entanglement entropy and spin variance correspond well with the semiclassical phase space. Our results imply that the correspondence principle is not invalidated by quantum collapse and revival effects in the large atom-light frequency ratios Rabi model.

We extend a well-known mass-gap equation for pure gluodynamics in global colour models (formulated in equal-time quantization in Coulomb gauge) to one in which gluons are split into two sets, each exhibiting different masses. If the theory is SU(N) × SU(M) with gluons in both groups having identical couplings (as suggested by Grand Unification arguments at large scales) it is immediate to see that different masses are generated for each subgroup. This global symmetry is not broken, but the split masses erase accidental symmetries that might be present due to the two couplings being the same at a large scale, such as SU(N × M) or similar. We also numerically explore a couple of low-dimensional examples of simple Lie groups, but in spite of the system of equations having a form that would seem to allow spontaneous symmetry breaking, it is not triggered for these groups whose algebra has no ideal, and the dispersion relations for the various gluons converge to the same form.

In this paper, we present the second post-Newtonian solution for the quasi-Keplerian motion of a test particle in the regular Simpson-Visser black-bounce spacetime which has a bounce parameter a. The obtained solution is formulated in terms of orbital energy, angular momentum, and the bounce parameter of the black hole. We explicitly analyze the leading effects of the bounce parameter which has dimensions of length, on the test particle's orbit, including the periastron advance and orbital period. Then, we apply this model to the precessing motion of OJ 287 and determine the upper limits of the dimensionless bounce parameter as a/m=3.45 ± 0.01, where m is the mass of the regular black hole. Compared with the bound given by the periastron advance of star S2, our bound on a/m is reduced by one order of magnitude, although our upper limit of a still needs further improvement.

Understanding the nature of dark matter remains one of the most enigmatic and unresolved issues in astrophysics. Certain theoretical models address this by introducing a novel component to account for dark matter. In this study, we propose a new scalar field derived from string T-duality, where its associated density represents the density of the surrounding matter field, in the spherically symmetric and static medium. Our exploration reveals that this scalar field behaves as the baryonic fluid, characterized by a positive effective state equation, ${\omega }_{{\rm{e}}}\gt 0$. Furthermore, a detailed investigation demonstrates that this model satisfies all energy conditions beyond the event horizon of a central black hole. Considering the light deflection and radar echo delay suggests that in this scalar field, the dark matter grows up in the halo and surrounding regions of galaxy systems. This indicates that dark matter accumulates as an effective field outside the observable regions of galaxies.

In this work, the phase structure of a holographic s+d model with quartic potential terms from 4D Einstein-Gauss-Bonnet gravity is studied in the probe limit. We first show the q_d-μ phase diagram with a very small value of the Gauss-Bonnet coefficient α=1 × 10^-7 and in the absence of the quartic terms to locate the suitable choice of the value of q_d, where the system admits coexistent s+d solutions. Then we consider the various values of the Gauss-Bonnet coefficient α and present the α-μ phase diagram to show the influence of the Gauss-Bonnet term on the phase structure. We also give an example of the re-entrant phase transition which is also realized in the holographic s+s and s+p models. After that we confirm the universality of the influence of the quartic term with coefficient λ_d on the d-wave solutions, which is similar to the case of s-wave and p-wave solutions previously studied in the s+p model. Finally we give the dependence of the special values of the quartic term coefficient λ_d on the Gauss-Bonnet coefficient α, below which the d-wave condensate grows to an opposite direction at the (quasi-)critical point, which is useful in realizing first order phase transitions in further studies of the holographic d-wave superfluids.

In this study, we proposed a bifunctional sensor of high sensitivity and slow light based on monolayer ${{\rm{MoS}}}_{2}/{\rm{TOPAS}}$ structure in the terahertz range. The proposed metamaterial is formed by a structured unit matrix that combines square and cross shapes made of ${{\rm{MoS}}}_{2}$ and ${\rm{TOPAS}}$. The plasmon-induced transparency (PIT) spectra appeared under the excitation of a transverse magnetic (TM)-polarization wave, the proposed PIT effect is originated from the near-field coupling of two bright modes. The Lorentzian mode theory spectrum describes the destructive interference between the two bright modes, and the fitted results are consistent with the Finite-Difference Time-Domain (FDTD) simulation results. Furthermore, the effect of geometrical sizes, like coupling distance, structure size, and intersection angle between square and cross shape on the PIT window is analyzed, along with the effects of carrier concentration in ${{\rm{MoS}}}_{2}$. A figure of merit of $1.10\,{{\rm{RIU}}}^{-1}$ is obtained. The slow light performance of the proposed ${{\rm{MoS}}}_{2}$-based metamaterial is investigated, a maximum time delay of $0.52\,{\rm{ps}}$ is obtained and the delay band width product (DBP) is 0.76. It is more efficient to store and transmit the information over signal channels. Therefore, the proposed ${{\rm{MoS}}}_{2}$-based metamaterial can be used in electromagnetically induced transparency applications, such as sensors, optical memory devices, and flexible terahertz functional devices.

The effects of the Rashba spin-orbit interaction and external electric and magnetic fields on the thermodynamic properties of parabolic quantum dots are investigated. An explicit partition function is derived, and thermodynamic quantities, including specific heat, entropy, and magnetic susceptibility, are analyzed. The behavior of Shannon entropy-related thermodynamic quantities is examined under varying magnetic fields and Hamiltonian parameters through numerical analysis. The results reveal a pronounced Schottky anomaly in the heat capacity at lower temperatures. The susceptibility exhibits a progressive enhancement and transitions to higher values with changes in the quantum dot parameters. In the presence of the Rashba spin-orbit interaction, the specific heat increases with temperature, reaches a peak, and then decreases to zero. Additionally, the susceptibility increases with the β parameter for varying Rashba spin-orbit interaction coefficients, and at a fixed temperature, it further increases with the Rashba coefficient.

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 transport 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 $\geqslant $ 0.1 μm² s^-1, can largely enhance the processivity relative to the non-diffusive cargo and relative to the cargo having no interaction with the track.

Computing free energy is a fundamental problem in statistical physics. Recently, two distinct methods have been developed and have demonstrated remarkable success: the tensor-network-based contraction method and the neural-network-based variational method. Tensor networks are accurate, but their application is often limited to low-dimensional systems due to the high computational complexity in high-dimensional systems. The neural network method applies to systems with general topology. However, as a variational method, it is not as accurate as tensor networks. In this work, we propose an integrated approach, tensor-network-based variational autoregressive networks (TNVAN), that leverages the strengths of both tensor networks and neural networks: combining the variational autoregressive neural network's ability to compute an upper bound on free energy and perform unbiased sampling from the variational distribution with the tensor network's power to accurately compute the partition function for small sub-systems, resulting in a robust method for precisely estimating free energy. To evaluate the proposed approach, we conducted numerical experiments on spin glass systems with various topologies, including two-dimensional lattices, fully connected graphs, and random graphs. Our numerical results demonstrate the superior accuracy of our method compared to existing approaches. In particular, it effectively handles systems with long-range interactions and leverages GPU efficiency without requiring singular value decomposition, indicating great potential in tackling statistical mechanics problems and simulating high-dimensional complex systems through both tensor networks and neural networks.

The elastic properties of membranes are typically characterized by a few phenomenological parameters, including bending and Gaussian curvature moduli measuring the membrane rigidity against its deformation and topological change, as well as spontaneous curvature arising from the asymmetry between the two leaflets in the lipid bilayers. Though tether-based and fluctuation-based experiments are commonly utilized to measure the bending modulus, measuring the Gaussian curvature modulus and the spontaneous curvature of the membrane is considered to be much more difficult. In this paper, we study the buckling process of a circular membrane with nonzero spontaneous curvature under compressive stresses. It is found that when the stress exceeds a critical value, the circular membrane will transform from a spherical cap to a buckled shape, with its buckling degree enhanced with the increase of stress until its base is constricted to almost zero. As the stress-strain relationship of the buckled membrane strongly depends on the Gaussian curvature modulus and the spontaneous curvature,we therefore propose a method to determine the Gaussian curvature modulus and the spontaneous curvature simultaneously by measuring its stress-strain relationship during a buckling process.

We investigate the chaotic and regular spatial structures of Bose-Einstein condensates (BECs) with a spatially modulated atom-atom interaction and without an external trapping potential. A BEC with a spatially modulated atom-atom interaction is equivalent to being constrained by a nonlinear optical lattice. Theoretical analyses show the existence of a steady atomic current in the BEC with a spatially varying phase. Under perturbative conditions, the Melnikov chaos criteria of BECs with a spatially varying phase and a constant one are theoretically obtained, respectively. When the perturbative conditions cannot be satisfied, for a repulsive BEC with a spatially varying phase, numerical simulations demonstrate that changing the initial condition can eliminate the chaotic spatial structure and then the system transitions into a biperiodic spatial structure. Increasing the chemical potential can result in a transition from the biperiodic spatial structure to a single-periodic spatial structure. For an attractive BEC with a spatially varying phase, numerical simulations show that decreasing the chemical potential can lead to a high atomic density, but when the wave number of the laser inducing the optical Feshbach resonance exceeds a critical value, the atomic density falls back to a finite range. Regardless of whether the BEC has a spatially varying phase or a constant one, modulating the laser wave number can effectively suppress the chaotic spatial structure in the BEC and then force it into a regular spatial structure.

This paper presents a tunable and polarization-insensitive wideband metamaterial absorber based on single-layer graphene. By comparing the simulated experimental data with theoretical derivations, 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 modify 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 the 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 tunability, a wide absorption band, a high absorption rate, polarization insensitivity, and a simple structure. Therefore, this absorber exhibits great potential for absorption, monitoring, and sensing in the terahertz band.

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.