One-dimensional Systems Research Articles

Topological semimetal phase in non-Hermitian Su–Schrieffer–Heeger model

We explore the non-Hermitian Su–Schrieffer–Heeger model with long-range hopping and off-diagonal disorders. In the non-Hermitian clean limit, we find that the phase diagram holds topological semimetal phase with exceptional points except the normal insulator phase and the topological insulator phase. Interestingly, it is found that the topological semimetal phase is induced by long-range nonreciprocal term when the long-range hopping is not equal to the intercell hopping. Especially, we show the existence of topological semimetal phase with exceptional points and determine the transition point analytically and numerically under the Hermitian clean limit when the long-range hopping is equal to the intercell hopping. Furthermore, we also investigate the effects of the disorders on topological semimetal phase, and show that the disorders can enhance the region of topological semimetal phase in contrast to the case of non-Hermitian clean limit, indicating that it is beneficial to topological semimetal phase whether there is one disorder or two disorders in the system, that is, the topological semimetal phase is stable against the disorders in this one-dimensional non-Hermitian system. Our work provides an alternative avenue for studying topological semimetal phase in non-Hermitian lattice systems.

Research on multi-beam problems based on geometric modeling and underwater detection

This paper aims to establish and solve the mathematical model of coverage width under multi-beam bathymetry, rising from a one-dimensional sea area measurement problem to a two-dimensional sea area measurement problem. First, this paper takes the center of the sea area as the coordinate origin, establishes a one-dimensional coordinate system, and derives the functional relationship between the coordinate position of the measured ship axis and the angle of the seabed slope through the triangle edge relationship. At the same time, the mathematical relationship between the depth of the water body and the position of the measuring ship is constructed, and the relationship between the single coverage width of the detection system and the depth of the water body is found using the sine theorem. Subsequently, this paper established a two-dimensional sea area measurement model. Taking the center point of the sea area to be measured as the coordinate origin, a three-dimensional coordinate system was constructed. The normal vector projection direction was taken into account to obtain the new slope angle, and the two-dimensional sea area measurement was converted into a one-dimensional sea area. Measurement. Finally, this article uses MATLAB to conduct simulation experiments and gives the relationship between the coverage width and the position of the survey ship at different angles between survey line directions, providing an effective reference for the multi-beam sounding strategy.

Exploring cone-shaped solitons, breather, and lump-forms solutions using the lie symmetry method and unified approach to a coupled breaking soliton model

In this research article, we investigate the coupled breaking soliton (cBS) model using two distinct analytical methods, namely, the Lie symmetry approach and the Unified method. We start by applying the Lie group technique to the cBS model, allowing us to establish infinitesimals, vector fields, commutative and adjoint tables, and an adjoint transformation matrix. Through the utilization of the adjoint transformation matrix, we identify a one-dimensional optimal system of subalgebras. This essential stage allows the cBS model to be reduced into several collections of ordinary differential equations (ODEs) relating to similarity variables resulting from symmetry reduction. By solving these ODE systems under specific parametric constraints, we successfully obtain exact solutions in terms of closed form. Furthermore, the Unified method is employed to address the governing equation, leading us to deduce polynomial and rational function solutions. The dynamic behaviours and characteristics of these such solutions are comprehensively explored through 3-dimensional (3D) plots and contour plots. The graphics show breather solitons, cone-shaped solitons, lump solitons, and patterns of flower petals, periodic solitons, and solitary waves. Additionally, we have connected our mathematical findings with real-world phenomena, which enrich our research work. Furthermore, breathers and lumps arise in many fields of mathematical physics, including fluid dynamics, plasma physics, ocean engineering, nonlinear optics, and physical sciences, as well as several other areas of nonlinear dynamics.

Spin current generation in an organic antiferromagnet via photo-excitation

We investigate the spin current generation in a one-dimensional organic antiferromagnetic system under light illumination via the quadratic response theory. We show that when the light energy is greater than the band gap of the system, a finite DC spin current of the shift type can be excited while the charge current remains zero. The spin conductivity is found to be an even function of the chemical potential μ, and can take comparatively large values around μ=0. The estimated nonlinear spin conductivity might be on the order of 10−6ħe⋅A/V2, which is comparable to the values reported recently for some inorganic systems, indicating that the optical approach may be an efficient way to generate spin currents in organic materials.

Existence analysis of a cross-diffusion system with nonlinear Robin boundary conditions for vesicle transport in neurites

A one-dimensional cross-diffusion system modeling the transport of vesicles in neurites is analyzed. The equations are coupled via nonlinear Robin boundary conditions to ordinary differential equations for the number of vesicles in the reservoirs in the cell body and the growth cone at the end of the neurite. The existence of bounded weak solutions is proved by using the boundedness-by-entropy method. Numerical simulations show the dynamical behavior of the concentrations of anterograde and retrograde vesicles in the neurite.

Influence of depressurization mode on natural gas hydrate production characteristics: One-dimensional experimental study

The latest research suggests that using depressurization methods and their enhancements could be the most effective way to produce natural gas hydrates efficiently in marine areas. Therefore, it's crucial to investigate the gas production behavior and the changes in temperature and pressure within natural gas hydrate reservoirs under different depressurization methods. In this paper, the self-developed one-dimensional natural gas hydrate production simulation test system was utilized to conduct one-dimensional depressurization production tests during two depressurization modes of significant depressurization and slow depressurization. The findings indicated that the minimum temperature increment-depressurization rate curves in significant depressurization tests exhibited irregular patterns, primarily due to the frequency and intensity of hydrate reformation, while the smaller the depressurization rate, the larger the minimum temperature increment and the smaller the maximum dissociation rate under slow depressurization. In addition, when maintaining a fixed hydrate saturation level, the peak gas production rate showed a decline with decreasing depressurization rate. However, the exact correlation between the peak gas production rate and the depressurization rate remained uncertain due to the unpredictable nature of the “armoring” effect.

Energy decay analysis for Porous elastic system with thermoelasticity of type III: A second spectrum approach

Numerous studies have been conducted to investigate porous systems under different damping effects. Recent research has consistently achieved the expected exponential decay of energy solutions when employing stabilization techniques that involve non-physical assumptions of equal wave velocities. In this study, we examine a one-dimensional thermoelastic porous system within the framework of the second frequency spectrum. Remarkably, we demonstrate that exponential decay can be achieved without relying on the assumption of equal wave speeds. We consider the porous system, and we incorporated thermoelastic damping based on the Green–Naghdi law of heat conduction into our study. To begin with, we use the Faedo–Galerkin approximation method to validate the global well-posedness of the system. By utilizing a Lyapunov functional, we establish exponential stability without relying on the assumption of equal wave speed. We then introduce and analyze a numerical scheme. Finally, by assuming additional regularity of the solution, we derive a priori error estimates.

High-order well-balanced numerical schemes for one-dimensional shallow-water systems with Coriolis terms

The goal of this work is to develop high-order well-balanced schemes for the one-dimensional shallow-water equations with Coriolis terms. The main contribution is the development of general numerical methods that allow the achievement of arbitrary high-order for the shallow-water equations with Coriolis terms while preserving all the stationary solutions.

Topological phase in one-dimensional momentum space lattice of ultracold atoms without chiral symmetry

Symmetry plays a crucial role in understanding topological phases in materials. In one-dimensional systems, such as the Su-Schrieffer-Heeger (SSH) model, chiral symmetry is thought to ensure the quantization of the Zak phase and the nontrivial topological phase. However, our work demonstrates that the one-dimensional lattice system with broken chiral symmetry can still possess quantized Zak phase and nontrivial topological phase. Specifically, we use a Bose-Einstein condensate of <sup>87</sup>Rb atoms in a momentum space lattice of ultracold atoms to effectively simulate a one-dimensional Zigzag model of 26 sites, which intrinsically breaks the chiral symmetry by additional next-nearest-neighbor coupling. To ensure the existence of the nontrivial topological phase, where the Zak phase can be measured from the time-averaged displacement during the system’s evolution, we need to preserve the inversion symmetry by modulating laser power so that all next-nearest-neighbor coupling strengths are equal. Furthermore, by changing the ratio of nearest-neighbor coupling strengths, we observe a topological phase transition from a nontrivial topological phase to a trivial topological phase at the point where the ratio equals 1. Our work demonstrates that the ultracold atom system provides a controllable platform for studying the symmetrical phase and topological phase, with the potential to explore nonlinear topological phenomena by increasing the interactions among atoms. In addition, our system can be used to investigate other interesting topological phenomena with more complex models, such as critical phenomena at the phase transitions and flat band structures in the extended SSH model with long-range coupling. By controlling the coupling strengths, we can also explore the influence of different symmetries on the topological properties of extended SSH models in the future. Moreover, our platform makes it possible to studythe models with more energy bands, such as the Aharonov-Bohm caging model with a three-level structure, which shows peculiar flat-band properties. This work provides opportunities for various studies in the fields of symmetry, topology, and the interaction of controllable quantum systems.

Well-Posedness and Asymptotic Stability of a Non-Linear Porous System with a Delay Term

Our interest in this work is to treat a one-dimensional Porous system with a non-linear damping and a delay in the non-linear internal feedback. We prove the global existence and uniqueness of its solution in suitable function spaces by means of the Faedo-Galerkin procedure combined with the energy method under a suitable relation between the weight of the delayed feedback and the weight of the non-delayed feedback. Also, we give an explicit and general decay rate estimate by applying the well-known multiplier method integrated with some properties of convex functions and for two opposites cases with respect to the speeds of wave propagation.

Spin-degree manipulation for one-dimensional room-temperature ferromagnetism in a haldane system.

The intricate correlation between lattice geometry, topological behavior and charge degrees of freedom plays a key role in determining the physical and chemical properties of a quantum-magnetic system. Herein, we investigate the introduction of the unusual oxidation state as an alternative pathway to modulate the magnetic ground state in the well-known S = 1 Haldane system nickelate Y2BaNiO5 (YBNO). YBNO is topologically reduced to incorporate d9-Ni+ (S = 1/2) in the one-dimensional Haldane chain system. The random distribution of Ni+ for the first time results in the emergence of a one-dimensional ferromagnetic phase with a transition temperature far above room temperature. Theoretical calculations reveal that the antiferromagnetic interplay can evolve into ferromagnetic interactions with the presence of oxygen vacancies, which promotes the formation of ferromagnetic order within one-dimensional nickel chains. The unusual electronic instabilities in the nickel-based Haldane system may offer new possibilities towards unconventional physical and chemical properties from quantum interactions.

Density functional theory study of the electronic and optical properties of pentagraphyne nanotubes.

Pentagraphyne (PG-yne), a recently predicted two-dimensional (2D) carbon allotrope with appealing properties, has opened up possibilities for a wide range of applications. In this study, we investigate the structural, electronic, optical, and electrical transport properties of a novel one-dimensional (1D) system called pentagraphyne nanotubes (PG-yneNTs), formed by rolling a PG-yne sheet, using density functional theory (DFT) calculations. We design PG-yneNTs with diameters ranging from 6.94 Å to 13.62 Å and employ state-of-the-art theoretical calculations to confirm their energetic, dynamic, and thermodynamic stability. Our electronic band structure calculations reveal that all these nanotubes are wide indirect band gap semiconductors. Remarkably, PG-yneNTs exhibit superior optical properties, including high absorption coefficients and absorption spectra covering the visible regime of the electromagnetic spectrum, making them potential candidates for visible-light-driven photocatalysis and solar cells. Interestingly, both the electronic and optical band gaps increase with the diameter of the nanotubes. Additionally, the observation of negative differential resistance (NDR) phenomena in (4, 0) PG-yneNT suggests their potential applications in NDR devices such as fast switches, frequency multipliers, and memory devices.

Localization transition in non-Hermitian coupled chain

In this paper, we study the properties of a coupled chain modulated by the quasiperiodic complex potential. It is found that as the disorder strength increases, the system undergoes a localization transition from a fully extended phase to an intermediate phase, and then to a fully localized phase. The numerical solving of order parameters such as the average inverse participation ratio and the average normalized participation ratio, demonstrate that the fully extended phase, the intermediate phase with mobility edges, and the fully localized phase are all existent during the transition. The scalar analysis of the normalized participation ratio, confirms the stable existence of three different localization phases in the system. Moreover, the analytical derivation, shows that the localization transition from the extended phase to the intermediate phase and from the intermediate phase to the localized phase can be precisely determined. In addition, the local phase diagram of the system is also obtained by numerical calculation, as shown in Fig. (a). The regions for the extended, intermediate and localized phases are denoted by I-a (I-b), II, and III, respectively. The three black solid lines represent the localization transition points determined by the analytical results. One can see that the analytical results match the numerical results. Moreover, we discuss that the relationship between the real-complex spectrum transition and the localization transition. It is found that the energy spectrum of the system can undergo two real-to-complex transitions. Specifically, during the transition from the fully extended phase to the intermediate phase, the first real-complex transition occurs, where part of the energy spectrum changes from the real spectrum to the complex spectrum, while another part spectrum remains real. When the system transitions from the intermediate phase to the fully localized phase, the energy spectrum completely transforms into a complex spectrum. These research results provide a reference for the study of localization transitions and real-complex transitions in one-dimensional coupled chain systems, and also offer a new perspective for the study of localization.

$ \mathcal{N} = 2 $ double graded supersymmetric quantum mechanics via dimensional reduction

<abstract><p>We presented a novel $ \mathcal{N} = 2 $ $ \mathbb{Z}_2^2 $-graded supersymmetric quantum mechanics ($ {\mathbb{Z}_2^2} $-SQM) which has different features from those introduced so far. It is a two-dimensional (two-particle) system and was the first example of the quantum mechanical realization of an eight-dimensional irreducible representation (irrep) of the $ \mathcal{N} = 2 $ $ \mathbb{Z}_2^2 $-supersymmetry algebra. The $ {\mathbb{Z}_2^2} $-SQM was obtained by quantizing the one-dimensional classical system derived by dimensional reduction from the two-dimensional $ {\mathbb{Z}_2^2} $-supersymmetric Lagrangian of $ \mathcal{N} = 1 $, which we constructed in our previous work. The ground states of the $ {\mathbb{Z}_2^2} $-SQM were also investigated.</p></abstract>

Технология повышения свойств робастного качества управления для одномерных линейных дискретных систем управления со структурно-параметрической неопределенностью

The article considers one-dimensional linear automatic control systems in discrete time. It is assumed that the operators of the control object contain parametric and/or structural uncertainty. The purpose of the study is to develop a method for the synthesis of modal controllers that provide the maximum robust quality of control of a closed system. The main result is presented in the form of an algorithm for improving the robust quality of control. The efficiency of the algorithm is illustrated by an example.

PROPAGATION OF SOLITON IN A ONE-DIMENSIONAL DISCRETE SYSTEM WITHIN SELF-ACTION MODE

Abstract. This study investigates the soliton propagation in a one-dimensional discrete system characterized by the Discrete Nonlinear Schrödinger Equation (DNLSE). The DNLSE is a fundamental model in wave phenomena, encompassing a broad spectrum of physical systems ranging from optics to fluid dynamics. The study uses both analytical and numerical computations to comprehensively observe the process. Through the analytical approach, i.e., the variation approximation (VA) method, essential parameters governing soliton evolutions, such as width, center-of-mass position, and linear and quadratic phase-front corrections are determined and graphically interpreted. These results are compared against direct numerical simulations of the main equation for validation. The results show that an increase in linear phase-front correction corresponds to an increase in both the soliton’s initial velocity and propagation distance. Additionally, direct numerical simulation reveals the increasing prominence of the discreteness effects with higher initial velocities.

Stability of a one-dimensional full viscous quantum hydrodynamic system

Stability of a one-dimensional full viscous quantum hydrodynamic system

Surface impedance and topologically protected interface modes in one-dimensional phononic crystals

When semi-infinite phononic crystals (PCs) are in contact, localized modes may exist at their boundary. The central question is generally to predict their existence and to determine their stability. With the rapid expansion of the field of topological insulators, powerful tools have been developed to address these questions. In particular, when applied to one-dimensional systems with mirror symmetry, the bulk-boundary correspondence claims that the existence of interface modes is given by a topological invariant computed from the bulk properties of the PC, which ensures strong stability properties. This one-dimensional bulk-boundary correspondence has been proven in various works. Recent attempts have exploited the notion of surface impedance, relying on analytical calculations of the transfer matrix. In the present work, the monotonic evolution of surface impedance with frequency is proven for all one-dimensional PCs with mirror symmetry. This result allows us to establish a stronger version of the bulk-boundary correspondence that guarantees not only the existence but also the uniqueness of a topologically protected interface state. This correspondence is extended to a larger class of one-dimensional models that include imperfect interfaces, array of resonators, or dispersive media. Numerical simulations are proposed to illustrate the theoretical findings.

Examining the Band Gap Structure of Nano-Electronic Devices, in Addition to Introducing a Method for Researching the Performance of One-Dimensional Systems <br>

Examining the Band Gap Structure of Nano-Electronic Devices, in Addition to Introducing a Method for Researching the Performance of One-Dimensional Systems <br>

Wavelength-selective thermal emission metasurfaces based on synthetic dimensional topological Weyl points

Blackbody emission such as the emission from incandescent sources usually possesses a broadband emission spectrum covering the whole infrared wavelength range. Most of emission energy goes into the unwanted infrared range and consequently causes low emission efficiency. Recently, metasurfaces with two-dimensional subwavelength artificial nanostructures have been widely studied due to their flexibility in modulating optical properties, thus providing an ideal platform for controlling thermal emission. The use of synthetic dimension methods in metasurfaces has opened up new avenues for fine-tuning thermal emission, especially highlighting the physical properties beyond traditional three-dimensional systems and rich topological physics. Although it is theoretically possible to explore physical phenomena through complete three-dimensional structures, such structures are difficult to construct in practice. In contrast, studying one-dimensional system or two-dimensional system is more feasible and efficient. The synthetic dimension approach introduces the possibility of manipulating intrinsic degrees of freedom in photon systems by introducing structural or physical parameters. In this work, we propose utilizing synthetic dimension methods to achieve wavelength-selective thermal emission. Firstly, we construct synthetic Weyl point in a superlattice model and validate it theoretically. Subsequently, experimental characterization of synthetic Weyl cones is conducted by using angle-resolved thermal emission spectroscopy (ARTES). The experimental results demonstrate that we can achieve reasonable wavelength-selective thermal emission while suppressing emission at other wavelengths as much as possible. This is essential for practical infrared applications such as thermalphotovoltaics and thermal management devices.