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.
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.
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.
In our study of super quantum discord between two excitonic qubits inside a coupled semiconductor quantum dots system, our primary focus is to uncover the impact of weak measurement on its quantum characteristics. To achieve this, we analyze how varying the measurement strength x, affects this super quantum correlation in the presence of thermal effects. Additionally, we assess the effect of this variation on the system's evolution against its associated quantum parameters; external electric fields, exciton–exciton dipole interaction energy and Förster interaction. Our findings indicate that adjusting x to smaller values effectively enhances the super quantum correlation, making weak measurements act as a catalyst. This adjustment ensures its robustness against thermal effects while preserving the non-classical attributes of the system. Furthermore, our study unveils that the effect of weak measurements on this latter surpasses the quantum effects associated with the system. Indeed, manipulating the parameter x allows the weak measurement to function as a versatile tool for modulating quantum characteristics and controlling exciton–exciton interactions within the coupled semiconductor quantum dots system.
The eikonal approximation (EA) is widely used in various high-energy scattering problems. In this work we generalize this approximation from the scattering problems with time-independent Hamiltonian to the ones with periodical Hamiltonians, i.e., the Floquet scattering problems. We further illustrate the applicability of our generalized EA via the scattering problem with respect to a shaking spherical square-well potential, by comparing the results given by this approximation and the exact ones. The generalized EA we developed is helpful for the research of manipulation of high-energy scattering processes with external field, e.g. the manipulation of atom, molecule or nuclear collisions or reactions via strong laser fields.
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.
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.
Photonic hyper-parallel quantum gates play a critical role in high-capacity quantum communication and fast quantum computing. Here, based on photon scattering in one-dimensional (1D) waveguides, we present some heralded schemes for constructing four-qubit hyper-controlled-not (hyper-CNOT) gates in two-photon systems. The qubits are encoded on both the polarization and spatial-mode degrees of freedoms (DOFs) of the photons, which can simplify the quantum circuit and reduce the quantum resource consumption. In our schemes, the faulty scattering events between photons and emitters caused by system imperfections can be filtered out and discarded. That is, our protocols for hyper-CNOT gates work in a heralded way. Our calculations show that, with great progress in the emitter-waveguide systems, our photonic hyper-CNOT gates may be experimentally feasible.
In this study, we examine the effects of weak gravitational lensing and determine the shadow radius around black holes within the Dyonic ModMax (DM) spacetime, also accounting for models with nonuniform plasma distributions. By analyzing various gravitational lens models, we compare corrections to vacuum lensing due to gravitational effects within plasma and plasma inhomogeneity, finding that these effects could be observed in hot gas within galaxy clusters. Starting with the orbits of photons around a black hole in DM, we investigate the shadow and weak gravitational lensing phenomena. Utilizing observational data from the Event Horizon Telescope for M87* and SgrA*, we constrain parameters within DM gravity. To connect our findings to observations, we examine the magnification and positioning of lensed images, along with the weak deflection angle and magnification for sources near different galaxies.
In this study, we examined the thermal fluctuations, deflection angle, and greybody factor of a high-dimensional Schwarzschild black hole in scalar–tensor–vector gravity (STVG). We calculated some thermodynamic quantities related to the correction of the black hole entropy caused by thermal fluctuations and discussed the effect of the correction parameters on these quantities. By analyzing the changes in the corrected specific heat, we found that thermal fluctuations made the small black hole more stable. It is worth noting that the STVG parameter did not affect the thermodynamic stability of this black hole. Additionally, by utilizing the Gauss–Bonnet theorem, the deflection angle was obtained in the weak field limit, and the effects of the two parameters on the results were visualized. Finally, we calculated the bounds on the greybody factor of a massless scalar field. We observed that as the STVG parameter around the black hole increased, the weak deflection angle became larger, and more scalar particles can reach infinity. However, the spacetime dimension has the opposite effect on the STVG parameter on the weak deflection angle and greybody factor.
A waveguide-QED with giant atoms, which is capable of accessing various limits of a small one, provides a new paradigm to study photon scatterings. Thus, how to achieve nonreciprocal photon transmissions via such a giant atom setup is highly desirable. In this study, the nonreciprocal single-photon scattering characteristics of a double-driven Λ-type three-level giant atom, where one of the transition couples to a 1D waveguide at two separate points, and the other is driven by two coherent driving fields, are investigated. It is found that a frequency-tunable single-photon diode with an ideal contrast ratio can be achieved by properly manipulating the local coupling phases between the giant atom and the waveguide, the accumulation phase between the two waveguide coupling points, the Rabi frequencies and phase difference of the two driven fields. Compared to the previous single driving schemes, on the one hand, the presence of the second driving field can provide more tunable parameters to manipulate the nonreciprocal single-photon scattering behavior. On the other hand, here perfect nonreciprocal transmission for photons with arbitrary frequencies is achievable by tuning the driving phases while the two driving fields keep on turning, which provides an alternative way to control the nonreciprocal single-photon scattering. Furthermore, the results reveal that both the location and width of each optimal nonreciprocal transmission window is also sensitive to the driving detuning, and a single-photon diode with wide or narrow bandwidth can be realized based on demand. These results may be beneficial for designing nonreciprocal single-photon devices based on a double-driven giant atom setup.
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.
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.
Most path integral expressions for quantum open systems are formulated with diagonal system-bath coupling, where the influence functional is a functional of scalar-valued trajectories. This formalism is enough if only a single bath is under consideration. However, when multiple baths are present, non-diagonal system-bath couplings need to be taken into consideration. In such a situation, using an abstract Liouvillian method, the influence functional can be obtained as a functional of operator-valued trajectories. The value of the influence functional itself also becomes a superoperator rather than an ordinary scalar, whose meaning is ambiguous at first glance and its connection to the conventional understanding of the influence functional needs extra careful consideration. In this article, we present another concrete derivation of the superoperator-valued influence functional based on the straightforward Trotter–Suzuki splitting, which can provide a clear picture to interpret the superoperator-valued influence functional.
Solar energy has always been a kind of energy with large reserves and wide application. It is well utilized through solar absorbers. In our study, the finite difference time domain method (FDTD) is used to simulate the absorber composed of refractory metal materials, and its absorption performance and thermal emission performance are obtained. The ultra-wide band of 200 nm–3000 nm reaches 95.93% absorption efficiency, of which the bandwidth absorption efficiency of 2533 nm (200 nm–2733 nm) is greater than 90%. The absorption efficiency in the whole spectrum range (200 nm–2733 nm) is 97.17% on average. The multilayer nanodisk structure of the absorber allows it to undergo strong surface plasmon resonance and near-field coupling when irradiated by incident light. The thermal emission performance of the absorber enables it to also be applied to the thermal emitter. The thermal emission efficiency of 95.37% can be achieved at a high temperature of up to 1500 K. Moreover, the changes of polarization and incident angle do not cause significant changes in absorption. Under the gradual change of polarization angle (0°–90°), the absorption spectrum maintains a high degree of consistency. As the incident angle increases from 0° to 60°, there is still 85% absorption efficiency. The high absorption efficiency and excellent thermal radiation intensity of ultra-wideband enable it to be deeply used in energy absorption and conversion applications.
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.
