Low-dimensional Systems Research Articles

Uncertainty relation and the constrained quadratic programming

The uncertainty relation is a fundamental concept in quantum theory, plays a pivotal role in various quantum information processing tasks. In this study, we explore the additive uncertainty relation pertaining to two or more observables, in terms of their variance, by utilizing the generalized Gell-Mann representation in qudit systems. We find that the tight state-independent lower bound of the variance sum can be characterized as a quadratic programming problem with nonlinear constraints in optimization theory. As illustrative examples, we derive analytical solutions for these quadratic programming problems in lower-dimensional systems, which align with the state-independent lower bounds. Additionally, we introduce a numerical algorithm tailored for solving these quadratic programming instances, highlighting its efficiency and accuracy. The advantage of our approach lies in its potential ability to simultaneously achieve the optimal value of the quadratic programming problem with nonlinear constraints but also precisely identify the extremal state where this optimal value is attained. This enables us to establish a tight state-independent lower bound for the sum of variances, and further identify the extremal state at which this lower bound is realized.

Optimal design of fast adiabatic topological pumping in modulated lattices

Utilizing synthetic dimensions generated by spatial or temporal modulation, topological pumping enables the exploration of higher-dimensional topological phenomena through lower-dimensional physical systems. In this Letter, we propose a rational design paradigm of fast adiabatic topological pumping based on 1D and 2D time-modulated discrete elastic lattices. First, the realization of topological pumping is ensured by introducing quantitative indicators to drive a transition of the edge or corner state in the lattice spectrum. Meanwhile, with the help of limiting speed for adiabaticity to calculate the modulation time, a mathematical formulation of designing topological pumping with the fastest modulation speed is presented. By applying the proposed design paradigm, topological edge–bulk–edge and corner–bulk–corner energy transport are achieved with 11.2 and 4.0 times of improvement in modulation speed compared to classical pumping systems in the literature. In addition, applying to 1D and 2D space-modulated systems, the optimized modulation schemes can reduce the number of stacks to 5.3% and 26.8% of the classical systems while ensuring highly concentrated energy transport. This design paradigm is expected to be extended to the rational design of fast topological pumping in other physical fields.

Static and resonant properties of decorated square kagomé lattice KCu[formula omitted](TeO[formula omitted])(SO[formula omitted])[formula omitted]Cl

The magnetic subsystem of nabokoite, KCu7(TeO4)(SO4)5Cl, is constituted by copper ions forming a buckled square kagomé lattice decorated by quasi-isolated ions. This combination determines peculiar physical properties of this compound evidenced in electron spin resonance (ESR) spectroscopy, dielectric permittivity ɛ, magnetization M and specific heat Cp measurements. At lowering temperature, the magnetic susceptibility χ=M/H passes through a broad hump inherent for low-dimensional magnetic systems at about 150 K and a sharp peak at antiferromagnetic phase transition at TN=3.2 K. The Cp(T,H) curves demonstrate additional peak-like anomaly at Tpeak=5.7 K robust to magnetic field. The latter can be ascribed to low-lying singlet excitations filling the singlet-triplet gap in magnetic excitation spectrum of the square kagomé lattice (Richter et al., 2022). ESR spectroscopy provides indications that antiferromagnetic structure below TN is non-collinear. Separate issue is the observation of antiferroelectric-type behavior in ɛ at low temperatures, which tentatively reduces the symmetry and partially lifts frustration of magnetic interactions of decorating copper ions with buckled square kagomé lattice. These complex thermodynamic and resonant properties signal the presence of two weakly coupled magnetic subsystems in nabokoite, namely a spin-liquid in square kagomé lattice layers and an antiferromagnet represented by decorating ions.

Probing rotated Weyl points on one-dimensional sonic crystals

Recently, researchers have devoted their intense efforts to investigating Weyl physics in synthetic space. In this Letter, we study the intriguing topological rotated Weyl physics in a three-dimensional parameter space, which consists of two extra structural parameters and the wave vector of a simple one-dimensional sonic crystal. In our ultrasonic experiments, we observe that the topological interface states propagate along the interface formed by two sonic crystals of distinct chirality caused by the rotated Weyl points. We detect the rotated synthetic Weyl points and measure the singularities of the reflection phase, which results in the robustness of the interface states. At the same time, it also shows the advantages of synthetic dimensions in exploring high-dimensional physics problems in low-dimensional systems.

Contribution of magnons created in volume and within the surface in low-dimensional dilute magnetic semiconductor: eTBA Calculation for [formula omitted

The magnetic properties in low-dimensional dilute magnetic semiconductor system (Sn1−xCoxO2) are studied in the framework of extended Tight Binding Approximation (eTBA). According to the parameters of the solid, we established the Schrödinger equation to a single spin-wave state constructed as a sum of Bloch of atomic-type individual states of creations of spin deviations on a given site. We developed a tight binding interatomic potential that essentially represents the combined effect of direct exchange J and the magneto-crystalline anisotropy Δ. We demonstrated the existence of two kinds of magnons created in volume and in the surface of the Sn1−xCoxO2/SiO2 multilayers. We calculated the excitation spectrum of these two kinds of magnons. The magnetization per spin is also obtained. The calculated values are in very satisfactory agreement with the experimental measurements.

Consideration of electronic mean heat transport via a low dimension system

The object of research is the complex realm of energy localization and coherent ballistic electronic transport within low-dimensional silicon quantum wires, specifically those doped with germanium atoms. Unlike their three-dimensional counterparts, low-dimensional systems exhibit unique electronic transport behaviors, necessitating novel analytical approaches for a comprehensive understanding. The core of this investigation leverages the Phase Field Matching Theory (PMFT) and the tight-binding (TB) approximation, sophisticated methodologies that enable a deep dive into the quantum mechanical nuances of these systems. Through this lens, we examine the intricate dynamics of dispersion relationships, phase factors, group velocities, and notably, the impact of defects introduced by the germanium doping. This research meticulously analyzes how these defects affect electronic and thermal conductivities, along with densities of states, offering new insights into the role of Fano resonances in the fluctuation of transmission and reflection spectra. These resonances, we find, are crucially dependent on the nature of the defects, their configuration, and the electronic parameters in their vicinity, underscoring the nuanced interplay between material composition and electronic properties in low-dimensional systems. The implications of our findings extend far beyond the theoretical. They pave the way for significant advancements in nanotechnology and the design of electronic devices, highlighting the potential for creating more efficient, high-performance components. Furthermore, this work proposes a framework for developing non-destructive testing methodologies that could revolutionize material science by enabling the precise analysis of defects in low-dimensional systems without causing damage. This is particularly critical for the ongoing development of materials with optimized properties for various applications, from electronics to energy storage. In essence, this research not only enriches our understanding of the physics governing low-dimensional systems but also offers practical insights into leveraging these properties for technological innovation. By bridging the gap between theoretical physics and material science, our study sets the stage for the next generation of electronic components and non-destructive evaluation techniques, marking a significant step forward in the application of quantum mechanics to real-world challenges.

Concomitant Light-Reversible Magnetic Response in Multiferroic Oxide Heterostructures for Multiphysics Applications.

The concept of multiphysics, where materials respond to diverse external stimuli, such as magnetic fields, electric fields, light irradiation, stress, heat, and chemical reactions, plays a fundamental role in the development of innovative devices. Nanomanufacturing, especially in low-dimensional systems, enhances the synergistic interactions taking place on the nanoscale. Light-matter interaction, rather than electric fields, holds great promise for achieving low-power, wireless control over magnetism, solving two major technological problems: the feasibility of electrical contacts at smaller scales and the undesired heating of the devices. Here, we shed light on the remarkable reversible modulation of magnetism using visible light in epitaxial Fe3O4/BaTiO3 heterostructure. This achievement is underpinned by the convergence of two distinct mechanisms. First, the magnetoelastic effect, triggered by ferroelectric domain switching, induces a proportional change in coercivity and remanence upon laser illumination. Second, light-matter interaction induces charged ferroelectric domain walls' electrostatic decompensations, acting intimately on the magnetization of the epitaxial Fe3O4 film by magnetoelectric coupling. Crucially, our experimental results vividly illustrate the capability to manipulate magnetic properties using visible light. This concomitant mechanism provides a promising avenue for low-intensity visible-light manipulation of magnetism, offering potential applications in multiferroic devices.

Charge-order melting in the one-dimensional Edwards model

We use infinite matrix-product-state techniques to study the time evolution of the charge-density-wave (CDW) order after a quench or a light pulse in a fundamental fermion-boson model. The motion of fermions in the model is linked to the creation of bosonic excitations, which counteracts the melting of the CDW order. For low-energy quenches corresponding to a change of the boson relaxation rate, we find behavior similar to that in an effective t−V model. When the boson energy is quenched instead or a light pulse is applied to the system, the transient dynamics are more complex, with the CDW order first quickly decreasing to an intermediate value while the density-wave-like order of the bosons rises. In the case of pulse irradiation, the subsequent time evolution of the CDW order depends strongly on the photon frequency. For frequencies slightly below the boson energy, we observe a temporary increase of the CDW order parameter. Our results reveal the complex physics of driven Mott insulators in low-dimensional systems with strong correlations. Published by the American Physical Society 2024

Robust photo-induced pure spin current in graphene–graphane superlattices

The photogalvanic effect has been demonstrated to be an effective method to generate pure spin current. However, obtaining robust pure spin current remains a big challenge as most of the photo-induced pure spin current is dependent on the light polarization/phase angle, photon energies, or the spin alignment of electrodes. In this paper, we present a scheme for obtaining robust pure spin current in zigzag graphene–graphane superlattices (ZGSLs). Through systemic first-principles calculations, we demonstrate that robust generation of pure spin current can occur in ZGSLs with varying widths due to the centrosymmetry of the system's geometric structure and the antiferromagnetic magnetic features. Moreover, the generation of pure spin current does not depend on the photon energy or the polarization/phase angles for both linearly and elliptically polarized light, exhibiting very strong robustness. Our study suggests that ZGSLs could be highly promising candidates for practically realizing pure spin current in spintronics experiments, which presents an avenue for using graphene and its derivatives in advanced electronic devices. Furthermore, considering the experimental advancements in graphene and graphene-like materials, our investigation presents a universally applicable methodology for the generation of robust pure spin currents within low-dimensional graphene-like systems.

Temperature-dependent optical bandgap of TiO2 under the Anatase and Rutile phases

A crucial step in developing new and/or more efficient devices relies on the detailed knowledge of the properties of their main (elemental or combined) parts. The same applies to titanium dioxide TiO2 that forms the basis of today numerous applications whose performances are determined by the presence or relative amount of the Anatase (A-) and Rutile (R-) most common phases of TiO2. Whereas the basic structural characteristics of these two polymorphs are very well-established, some of their optical aspects still deserve attention. With these ideas in mind this work presents a comprehensive investigation of the optical bandgap Egap of TiO2 under the Anatase and Rutile phases. The study considered pure A-TiO2 and R-TiO2 samples in the form of powder, and optical reflectance and Raman spectroscopy in the 83–823 K temperature range. In addition to reliable Egap values the study explores their temperature-dependent Egap(T) behavior that is expected to assist future advancements in the field of TiO2-based materials and devices (thin films, interfaces, low-dimensional systems, and photocatalytic and solar cells, for example).

Exact solutions to the fractional complex Ginzburg-Landau equation with cubic-quintic and Kerr law nonlinearities

The fractional complex cubic-quintic Ginzburg-Landau equation (FCCQGLE) with variable coefficients is a propagation model of optical pulses in optical fibers, the quintic term contained in it not only explains the physical significances that are not found in the existing models, but also has more abundant dynamic characteristics compared with lower dimensional systems. In this paper, the exact solutions of this equation are obtained via the appropriate transformations methods, which also are divided into different kinds. More precisely, we acquire the solitary, soliton and elliptic waves solutions by using the improved unified method, the bright and dark solitons solutions by using the improved F-expansion method, as well as the traveling wave solutions through the improved (G′/G2) -expansion and Bernoulli sub-equation function methods. Furthermore, we draw the 3D, 2D, density and contour plots to understand the propagation forms and the changes of amplitudes, frequencies and shapes of the solutions for the FCCQGLE with variable coefficients. The last thing worth mentioning is that the improved unified method here extends the degree of the polynomial from n to -n in the hypothetical solutions, which is not appeared before.

An algorithm based on 6D fractional order hyperchaotic system and knight tour algorithm to encrypt image

Abstract The security guarantee of data transmission is becoming more crucial as the frequency of information interchange rises. Ensuring the security of images is essential since they serve as a vital transmission medium. This research suggests an image encryption method that combines the knight tour algorithm with a 6D fractional order hyperchaotic system. First, chaotic sequences are produced using a fractional order hyperchaotic system, which is then utilized to index order and jumble the entire image. To retrieve the image after the second scrambling, choose the knight tour beginning point and run ten rounds of knight tour algorithms on the scrambled image. Thirdly, to maximize the efficiency of picture encryption, employ diffusion methods. The outcomes of the imaging experiment were lastly tested and assessed. The security of the image can be successfully guaranteed by a high-dimensional fractional order hyperchaotic system. This is because its high dimensionality gives it a larger key space than the low dimensional system. This is why it can resist attacks more effectively. After a series of evaluation experiments, it is obvious that this encryption scheme has good encryption performance.

Large-time lump patterns of Kadomtsev-Petviashvili I equation in a plasma analyzed via vector one-constraint method

In plasma physics, the Kadomtsev–Petviashvili I (KPI) equation is a fundamental model for investigating the evolution characteristics of nonlinear waves. For the KPI equation, the constraint method is an effective tool for generating solitonic or rational solutions from the solutions of lower-dimensional integrable systems. In this work, various nonsingular, rational lump solutions of the KPI equation are constructed by employing the vector one-constraint method and the generalized Darboux transformation of the (1 + 1)-dimensional vector Ablowitz–Kaup–Newell–Segur system. Furthermore, we investigate the large-time asymptotic behavior of high-order lumps in detail and discover distinct types of patterns. These lump patterns correspond to the high-order rogue wave patterns of the (1 + 1)-dimensional vector integrable equation and are associated with root structures of generalized Wronskian–Hermite polynomials.

An image encryption scheme based on the four-dimensional chaotic system and the mealy finite state machine

This paper proposes a four-dimensional hyperchaotic system to overcome the defect of weak encryption effect due to the simple complexity of low-dimensional chaotic systems in chaos-based image encryption schemes, which is verified to have better chaotic properties by dynamics analysis, sensitivity analysis, and randomness test. In addition, this paper proposes an image encryption scheme by combining the proposed chaotic system with the Mealy finite state machine (MFSM) to overcome the problem that some schemes are not resistant to statistical analysis. Firstly, the chaotic sequence is applied in the Knuth-Durstenfeld shuffling method to scramble the original image efficiently; secondly, according to the different information contained in the bit-plane, the pixel is decomposed and cyclically shifted at the bit level to achieve bit-level scrambling and diffusion; thirdly, the chaotic sequence is applied to select the rules for DNA encoding, and the diffusion process is achieved by Mealy finite state machine transformation; lastly, decoding the diffused image by selecting DNA rules randomly to get cipher image. This paper gives the experimental results, demonstrating that the scheme is highly secure. It can improve the encryption scheme’s sensitivity to plaintext and resist attacks such as differential attacks and select attacks.

Real-space blocking of qubit variables on parallel lattice gauge theory links for quantum simulation

One of the methods proposed in recent years for studying nonperturbative gauge theory physics is quantum simulation, where lattice gauge theories are mapped onto quantum devices which can be built in the laboratory, or quantum computers. While being very promising and already showing some experimental results, these methods still face several challenges related to the interface between the technological capabilities and the demands of the simulated models; in particular, one such challenge is the need to simulate infinitely dimensional local Hilbert spaces, describing the gauge fields on the links in the case of compact Lie gauge groups, requiring some truncations and approximations which are not completely understood or controllable in the general case. This work proposes a way to obtain arbitrarily large such local Hilbert spaces by using coarse graining of simple, low-dimensional qubit systems, made of components available on most quantum simulation platforms, and thus opening the way to new types of lattice gauge theory quantum simulations. Published by the American Physical Society 2024

Reanalysis of energy band structure in the type-II quantum wells

Band structure analysis holds significant importance for understanding the optoelectronic characteristics of semiconductor structures and exploring their potential applications in practice. For quantum well structures, the energy of carriers in the well splits into discrete energy levels due to the confinement of barriers in the growth direction. However, the discrete energy levels obtained at a fixed wave vector cannot accurately reflect the actual energy band structure. In this work, the band structure of the type-II quantum wells is reanalyzed. When the wave vectors of the entire Brillouin region (corresponding to the growth direction) are taken into account, the quantized energy levels of the carriers in the well are replaced by subbands with certain energy distributions. This new understanding of the energy bands of low-dimensional structures not only helps us to have a deeper cognition of the structure, but also may overturn many viewpoints in traditional band theories and serve as supplementary to the band theory of low-dimensional systems.

Fine-Tuning of the Excitonic Response in Monolayer WS2 Domes via Coupled Pressure and Strain Variation.

We present a spectroscopic investigation of the vibrational and optoelectronic properties of WS2 domes in the 0-0.65 GPa range. The pressure evolution of the system morphology, deduced by the combined analysis of Raman and photoluminescence spectra, revealed a significant variation in the dome's aspect ratio. The modification of the dome shape caused major changes in the mechanical properties of the system resulting in a sizable increase of the out-of-plane compressive strain while keeping the in-plane tensile strain unchanged. The variation of the strain gradients drives a nonlinear behavior in both the exciton energy and radiative recombination intensity, interpreted as the consequence of a hybridization mechanism between the electronic states of two distinct minima in the conduction band. Our results indicate that pressure and strain can be efficiently combined in low dimensional systems with unconventional morphology to obtain modulations of the electronic band structure not achievable in planar crystals.

A numerical study of rigidity of hyperbolic splittings in simple two-dimensional maps

Chaotic hyperbolic dynamical systems enjoy a surprising degree of rigidity, a fact which is well known in the mathematics community but perhaps less so in theoretical physics circles. Low-dimensional hyperbolic systems are either conjugate to linear automorphisms, that is, dynamically equivalent to the Arnold cat map and its variants, or their hyperbolic structure is not smooth. We illustrate this dichotomy using a family of analytic maps, for which we show by means of numerical simulations that the corresponding hyperbolic structure is not smooth, thereby providing an example for a global mechanism which produces non-smooth phase space structures in an otherwise smooth dynamical system.

Qudit machine learning

We present a comprehensive investigation into the learning capabilities of a simple d-level system (qudit). Our study is specialized for classification tasks using real-world databases, specifically the Iris, breast cancer, and MNIST datasets. We explore various learning models in the metric learning framework, along with different encoding strategies. In particular, we employ data re-uploading techniques and maximally orthogonal states to accommodate input data within low-dimensional systems. Our findings reveal optimal strategies, indicating that when the dimension of input feature data and the number of classes are not significantly larger than the qudit’s dimension, our results show favorable comparisons against the best classical models. This trend holds true even for small quantum systems, with dimensions d < 5 and utilizing algorithms with a few layers ( L=1,2 ). However, for high-dimensional data such as MNIST, we adopt a hybrid approach involving dimensional reduction through a convolutional neural network. In this context, we observe that small quantum systems often act as bottlenecks, resulting in lower accuracy compared to their classical counterparts.

A novel accelerated convergence method for solving adjoint equations based on modal reduction

The efficiency of adjoint-based aerodynamic shape optimization depends critically on the solution efficiency of adjoint equations. In this letter, we employ the Proper Orthogonal Decomposition (POD) method to analyze the adjoint field samples and project them from the physical space into a low-order modal space. Subsequently, the full-order adjoint equations are reduced to low-order equations using the POD modes. Thus, we can efficiently predict the initial values for pseudo-time marching, thereby accelerating the solution of adjoint equations. Results indicate that the high-order POD modes are crucial for constructing the low-dimensional system. Moreover, this method can be seamlessly integrated with our previously established Dynamic Mode Decomposition (DMD) acceleration method to form a POD+DMD acceleration approach. Application of this approach to the flow past a National Advisory Committee for Aeronautics 0012 airfoil demonstrates a noteworthy 80.9% reduction in iteration numbers when solving the adjoint equations. Even for the airfoil located on the upper boundary of sampling space, the number of iterations is still reduced by 72.6%. Therefore, we believe that the proposed method holds significant promise for improving the efficiency of adjoint-based aerodynamic shape optimization in future research.