Nearest-neighbor Approximation Research Articles

The band structure of a chain of periodically ordered different quantum dots

The paper introduces a model for a superlattice comprising periodically arranged quantum dots (QDs) and proposes a method for calculating the energy spectrum. This theory was applied to a chain of QDs. The study employed the effective mass approximation and solved the Schrödinger equation using the tight-binding model and nearest neighbor approximation. The energy spectra of electrons were determined as functions of the wave vector, and the theory facilitated the calculation of dispersion dependencies and bandwidths. The presence of different QDs resulted in the subdivision of the mini-zone into upper and lower zones. It was demonstrated and analyzed that the width of the upper zones consistently exceeds that of the lower ones. Furthermore, when the QDs possess identical sizes and materials, no forbidden zone is observed.

Antiferromagnitnyy eksitonnyy dielektrik

The effective the two-band Hamiltonian is obtained for iridium oxides with account for strong electron correlations (SEC) and the spin–orbit interaction. The intraatomic electron correlations in iridium ions induce the formation of Hubbard fermions (HF) filling the states in the valence band. Another consequence of SEC is associated with the emergence of the antiferromagnetic (AFM) exchange interaction between HF in accordance with the Anderson mechanism. As a result, a long-range antiferromagnetic order is established in the system, and in the conditions of band overlapping, the intersite Coulomb interaction induces a phase transition to the excitonic insulator (EI) state with a long-range AFM order. The system of integral self-consistent equations, the solution to which determines the excitonic order parameter components Δi, j(k), sublattice magnetization M, Hubbard fermion concentration nd, and chemical potential μ, is obtained using the atomic representation, the method of two-time temperature Green’s functions, and the Zwanzig–Mori projection technique. The symmetry classification of AFM EI phases is performed, and it is shown that in the nearest neighbor approximation, state Δi, j(k) with the s-type symmetry corresponds to the ground state, while the phases with the d- and p-symmetries are metastable.

Exploring plasmonic effect on exciton transport: A theoretical insight from macroscopic quantum electrodynamics.

Exciton transport in extended molecular systems and how to manipulate such transport in a complex environment are essential to many energy and optical-related applications. We investigate the mechanism of plasmon-coupled exciton transport by using the Pauli master equation approach, combined with kinetic rates derived from macroscopic quantum electrodynamics. Through our theoretical framework, we demonstrate that the presence of a silver nanorod induces significant frequency dependence in the ability of transporting exciton through a molecule chain, indicated by the exciton diffusion coefficient, due to the dispersive nature of the silver dielectric response. Compared with the same system in vacuum, great enhancement (up to a factor of 103) in the diffusion coefficient can be achieved by coupling the resonance energy transfer process to localized surface plasmon polariton modes of the nanorod. Furthermore, our analysis reveals that the diffusion coefficients with the nearest-neighbor coupling approximation are ∼10 times smaller than the results obtained beyond this approximation, emphasizing the significance of long-range coupling in exciton transport influenced by plasmonic nanostructures. This study not only paves the way for exploring practical approaches to study plasmon-coupled exciton transport but also provides crucial insights for the design of innovative plasmon-assisted photovoltaic applications.

Combined Radar and Communications With Phase-Modulated Frequency Permutations

This paper focuses on the combined radar and communications problem and conducts a thorough analytical investigation on the effect of phase and frequency change on the communication and sensing functionality. First, we consider the classical stepped frequency radar waveform and modulate data using M-ary phase shift keying (MPSK). Two important analytical tools in radar waveform design, namely the ambiguity function (AF) and the Fisher information matrix (FIM) are derived, based on which, we make the important conclusion that MPSK modulation has a negligible effect on radar local accuracy. Next, we extend the analysis to incorporate frequency permutations and propose a new signalling scheme in which the mapping between incoming data and waveforms is performed based on an efficient combinatorial transform called the Lehmer code. We also provide an efficient communications receiver based on a modified Hungarian algorithm. From the communications perspective, we consider the optimal maximum likelihood (ML) detector and derive the union bound and nearest neighbour approximation on the block error probability. From the radar sensing perspective, we discuss the broader structure of the waveform based on the AF derivation and quantify the radar local accuracy based on the FIM. Extensive numerical examples are provided to illustrate the accuracy of our results.

NON-DESTRUCTIVE CONTROL OF PVD COATING SURFACE DEFECTS

Nanostructured ZrN coatings were deposited by the vacuum arc method with partial separation of the plasma flow from macroparticles using a curvilinear magnetic filter. With the proposed deposition parameters, a ZrN coating with an fcc lattice and (111) texture is formed. Theoretical studies are carried out to assess the defects of the surface layer in the presence of an adsorbed impurity of an fcc lattice with the surface orientation plane (111), and the characteristics of surface waves in the ZrN coating are considered. Equations are obtained for the dispersion laws and parameters of the splitting off of the surface wave from the zone of bulk vibrations in the nearest-neighbor approximation.

Exciton transport in a moiré potential: From hopping to dispersive regime

The propagation of excitons in transition metal dichalcogenide (TMD) monolayers has been intensively studied revealing interesting many-particle effects, such as halo formation and nonclassical diffusion. Initial studies have investigated how exciton transport changes in twisted TMD bilayers, including Coulomb repulsion and Hubbard-like exciton hopping. In this work, we investigate the twist-angle dependent transition of the hopping regime to the dispersive regime of effectively free excitons. Based on a microscopic approach for excitons in the presence of a moir\'e potential, we show that the hopping regime occurs up to an angle of approximately ${2}^{\ensuremath{\circ}}$ and is well described by a moir\'e intercell tunneling model. At large angles, however, this nearest-neighbor approximation fails due to increasingly delocalized exciton states. Here, the quantum-mechanical dispersion of free particles with an effective mass determines the propagation of excitons. Overall, our work provides microscopic insights into the character of exciton propagation in twisted van der Waals heterostructures.

Nearest-neighbor approximation in one-excitation state evolution along spin-1/2 chain governed by XX-Hamiltonian

The approximation of nearest neighbor interaction (NNI) is widely used in short-time spin dynamics with dipole-dipole interactions (DDI) when the intensity of spin-spin interaction is ∼1/r3, where r is a distance between those spins. However, NNI can not approximate the long time evolution in such systems. We consider the system with the intensity of the spin-spin interaction ∼1/rα, α≥3, and find the low boundary αc of applicability of the NNI to the evolution of an arbitrary one-excitation initial quantum state in the homogeneous spin chain governed by the XX-Hamiltonian. We obtain the logarithmic dependence of αc on the chain length.

Frequency Permutations for Joint Radar and Communications

This paper presents a new joint radar and communication technique based on the classical stepped frequency radar waveform. The randomization in the waveform, which is achieved by using permutations of the sequence of frequency tones, is utilized for data transmission. A new signaling scheme is proposed in which the mapping between incoming data and waveforms is performed based on an efficient combinatorial transform called the Lehmer code. Considering the optimum maximum likelihood detection, the union bound and the nearest neighbour approximation on the communication block error probability is derived for communication in an additive white Gaussian noise channel. The results are further extended to incorporate the Rician fading channel model, of which the Rayleigh fading channel is presented as a special case. Furthermore, an efficient communication receiver implementation is discussed based on the Hungarian algorithm which achieves optimum performance with much less operational complexity when compared to an exhaustive search. From the radar perspective, two key analytical tools, namely, the ambiguity function and the Fisher information matrix are derived. Furthermore, accurate approximations to the Cramer-Rao lower bounds on the delay and Doppler estimation errors are derived based on which the range and velocity estimation accuracy of the waveform is analysed.

Modeling of Spin Crossover in Linear Trinuclear Complexes: Effects of External Pressure.

In the present study, a model is suggested to explain the course of spin transformation in crystals containing linear trinuclear iron(II) clusters as structural units. The energy spectrum of an isolated trimer is described with due allowance of the effects of the cubic crystal field formed by the nearest surrounding of each FeII ion as well as by consideration of intracluster interactions in the nearest neighbor approximation. The intercluster cooperative interaction promoting the spin transition is assumed to arise from the coupling of molecular modes with phonons, that is, a feature characteristic for molecular crystals containing as a structural element single spin-crossover ions or complexes formed by these ions. It is demonstrated that in dependence on the relative strengths of intra- and intercluster interactions, the trinuclear systems can exhibit a variety of different types of spin transitions and, namely, gradual, step-like transitions and those characterized by a hysteresis loop. The effects of external pressure on the spin transitions in crystals of trinuclear clusters are explored taking into account that pressure affects both the energy gap between the high-spin and low-spin states and the characteristic parameters of cooperative interaction. In the framework of the suggested model, the spin transformation in the Fe3(bntrz)6(tcnset)6 compound is comprehensively explained. The model also allows a qualitative and quantitative reproduction of the temperature and course of the spin transition in this compound under applied pressure.

Spin-dependent transport and spin transfer torque in a system based on silagraghene nanoribbons

We theoretically investigate the spin-dependent transport and spin transfer torque ( S T T ) in a system composed of a silagraphene nanoribbon ( S L N R ) connected to two ferromagnetic ( F M ) leads with arbitrary relative magnetization direction, using the tight-binding model in the nearest neighbor approximation within the framework of the Green function’s technique and Landauer–Butticer formalism. We report numerical calculation results for conductance ( G ), magnetoresistance ( M R ), and spin transfer torque ( S T T ) in the F M / S L N R / F M junction for different strengths of ferromagnetic magnetization. It is found that the G and M R show oscillatory behavior around E F = 0 and more interestingly, the magnitude of the M R reaches up to % 100 , which can be effectively used for sensitive switchings. In addition, it is demonstrated that S T T versus Fermi energy shows noticeable peaks with moving away from Dirac point energy. The results show that the torques as a function of the angle between two magnetic electrodes ( θ ) show a s i n -like behavior and the G − θ curve demonstrates approximately a c o s i n e -like behavior, which is a function of M . Our results can provide valuable theoretical guidance to design future novel spintronic devices. • We report the spin-polarized transport in a system based on silagraphene. • Our system consists of a silagraphene nanoribbon connected to two ferromagnetic electrodes (FM/Silagraphene/FM). • We employ Green function’s technique and Landauer–Butticer formalism. • We consider the conductance, magnetoresistance and spin transfer torque in this system for different strengths of ferromagnetic magnetization. • Our results demonstrate that the G, MR and STT show oscillatory behavior around Dirac point. • We found the n-type impurity is more suitable for dopping the system.

A real-time mix-adjusted median property price index enabled by an efficient nearest neighbour approximation data structure

Homeowners, first-time buyers, banks, governments and construction companies are highly interested in following the state of the property market. Currently, property price indexes are published several months out of date and hence do not offer the up-to-date information which housing market stakeholders need in order to make informed decisions. In this article, we present an enhanced version of a mix-adjusted median based property price index which uses geospatial property data and stratification in order to compare similar houses sold in different trading periods. The expansion of the algorithm to include additional parameters, enabled by both a richer dataset and the introduction of a new, efficient data structure for nearest neighbour approximation, allows for the construction of a far smoother and more robust index than the original algorithm produced.

M-neighbor approximation in one-qubit state transfer along zigzag and alternating spin-1/2 chains

We consider the M-neighbor approximation in the problem of one-qubit pure state transfer along the N-node zigzag and alternating spin chains governed by the XXZ-Hamiltonian with the dipole-dipole interaction. We show that always M > 1, i.e., the nearest neighbor approximation is not applicable to such interaction. Moreover, only all-node interaction (M = N − 1) properly describes the dynamics in the alternating chain. We reveal the region in the parameter space characterizing the chain geometry and orientation which provide the high-probability state-transfer. The optimal state-transfer probability and appropriate time instant for the zigzag and alternating chains are compared.

On the Validity of the Tight-Binding Method for Describing Systems of Subwavelength Resonators

The goal of this paper is to relate the capacitance matrix formalism to the tight-binding approximation. By doing so, we open the way to the use of mathematical techniques and tools from condensed matter theory in the mathematical and numerical analysis of metamaterials, in particular for the understanding of their topological properties. We first study how the capacitance matrix formalism, both when the material parameters are static and modulated, can be posed in a Hamiltonian form. Then, we use this result to compare this formalism to the tight-binding approximation. We prove that the correspondence between the capacitance formulation and the tight-binding approximation holds only in the case of dilute resonators. On the other hand, the tight-binding model is often coupled with a nearest-neighbor approximation, whereby long-range interactions are neglected. Even in the dilute case, we show that long-range interactions between subwavelength resonators are relatively strong and nearest-neighbor approximations are not generally appropriate.

Giant density-of-states van Hove singularities in the face-centered cubic lattice

All van Hove singularities in the density of states (DOS) of face-centered cubic lattice in the nearest and next-nearest neighbor approximation, focusing on higher-order ones, are found and classified. At special values of the ratio τ of nearest (t) and next-nearest neighbor hopping integral t′ giant DOS singularities, caused by van Hove lines or surfaces, are formed. An exact formula for DOS which provides efficient numerical implementation is proposed. The standard tetrahedron method is demonstrated to be inapplicable due to its poor convergence in the vicinity of kinks caused by van Hove singularities. A comparison with the case of large space dimensionality (infinite coordination number) including next-nearest neighbors is performed.

A text-embedding-based approach to measuring patent-to-patent technological similarity

This paper describes an efficiently scaleable approach to measuring technological similarity between patents by combining embedding techniques from natural language processing with nearest-neighbor approximation. Using this methodology, we are able to compute similarities between all existing patents, which in turn enables us to represent the whole patent universe as a technological network. We validate both technological signature and similarity in various ways and, using the case of electric vehicle technologies, demonstrate their usefulness in measuring knowledge flows, mapping technological change, and creating patent quality indicators. This paper contributes to the growing literature on text-based indicators for patent analysis. We provide thorough documentation of our methods, including all code, and indicators at https://github.com/AI-Growth-Lab/patent_p2p_similarity_w2v).

Двумерные электроны низкой плотности в магнитном поле

The photoluminescence spectrum from the two-dimensional low density electrons with the localized valence-band holes in magnetic field is studied. The ground state is considered as Wigner crystal ore the strongly correlated electron system. For the quantum Wigner crystal the Landau levels for vacancions (quasiholes appearing in the process of photoluminescence) are calculated in the quasiclassical approximation. The spectrum of single-particle excitations for a triangular lattice in the nearest-neighbor approximation is used. It is found that Landau levels for vacancions depend unusually on magnetic field. For the electron system with strong Coulomb interaction the Mahan exciton effect in the photoluminescence for the two-dimensional electrons in magnetic field is considered.

Two-dimensional low density electrons in high magnetic field

The photoluminescence spectrum from the two-dimensional low density electrons with the localized valence-band holes in magnetic field is studied. The ground state is considered as Wigner crystal ore the strongly correlated electron system. For the quantum Wigner crystal the Landau levels for vacancions (quasiholes appearing in the process of photoluminescence) are calculated in the quasiclassical approximation. The spectrum of single-particle excitations for a triangular lattice in the nearest-neighbor approximation is used. It is found that Landau levels for vacancions depend unusually on magnetic field. For the electron system with strong Coulomb interaction the Mahan exciton effect in the photoluminescence for the two-dimensional electrons in magnetic field is considered. Keywords: Wigner crystal, magnetic field, Mahan exciton, correlated electrons.

Spectral properties of Andreev crystals

We present an exhaustive study of Andreev crystals (ACs) -- quasi-one-dimensional superconducting wires with a periodic distribution of magnetic regions. The exchange field in these regions is assumed to be much smaller than the Fermi energy. Hence, the transport through the magnetic region can be described within the quasiclassical approximation. In the first part of the paper, by assuming that the separation between the magnetic regions is larger than the coherence length, we derive the effective nearest-neighbour tight-binding equations for ACs with a helical magnetic configuration. The spectrum within the gap of the host superconductor shows a pair of energy-symmetric bands. By increasing the strength of the magnetic impurities in ferromagnetic ACs, these bands cross without interacting. However, in any other helical configuration, there is a value of the magnetic strength at which the bands touch each other, forming a Dirac point. Further increase of the magnetic strength leads to a system with an inverted gap. We study junctions between ACs with inverted spectrum and show that junctions between (anti)ferromagnetic ACs (always) never exhibit bound states at the interface. In the second part, we extend our analysis beyond the nearest-neighbour approximation by solving the Eilenberger equation for infinite and junctions between semi-infinite ACs with collinear magnetization. From the obtained quasiclassical Green functions, we compute the local density of states and the local spin polarization in anti- and ferromagnetic ACs. We show that these junctions may exhibit bound states at the interface and fractionalization of the surface spin polarization.

Gate potential-controlled current switching in graphene Y-junctions

In this work we investigate the ballistic transport of electrons through three-terminal graphene-based devices. The system consists of a Y-shaped junction formed by three armchair-edged graphene nanoribbons with a rectangular gate potential applied to one of the output branches, whereby current control can be established by the controlling of the refractive index in graphene p–n junctions. Transport properties are obtained by using the Landauer–Büttiker formalism and the tight-binding model within the nearest-neighbor approximation, which allows the calculation of the conductance as function of the Fermi energy, the applied potential, and the system size, as well as the current density. The results demonstrate that the applied electric field can tune the current transmission between the input and two output leads and, consequently, the proposed system acts as a current switch.

Electrical transport and rectification in a typical heterostructure based on fullerene–pentacene suspended to copper leads

In this work, we study quantum electrical transport through a heterojunction molecular bridge based on a fullerene and a pentacene as an electron-poor and electron-rich, respectively, coupled to two copper semi-infinite electrodes. Our calculations are based on the Green’s function approach within the nearest-neighbor tight-binding approximation. For this reason, a theoretical generalized derivation is introduced to calculate the self-energy of a centered-cubic lattice electrode using a unitary transformation. Based on this model, the effects of different geometrical ways of contacts and also various values of the applied gate voltage are examined, comprehensively. The estimations obviously clarify that the value of the transmission coefficient of carriers for single contact is significantly different from multiple contacts, particularly near to the Fermi level. The model predicts that tunable rectification can be achieved via gate voltage and also different ways of coupling of the C $$_{60}$$ to the electrode. The reification ratio value of the device with six contacts of the C $$_{60}$$ molecule to the left electrode approaches over than 1400, when the gate voltage of 2.0 V is applied. The results can be applied in electronic devices and logic circuits based on molecular diodes.