Green Function Research Articles

Quantum scattering in one-dimensional periodic structures: A Green's function approach solved through continued fractions

Quantum scattering in one-dimensional periodic structures: A Green's function approach solved through continued fractions

Enhanced thermoelectric properties in hybrid graphane/graphene nanoribbons

The thermoelectric properties of hybrid graphane and graphene nanoribbons (GGNRs) are studied by the Landauer formula within the atomistic non-equilibrium Green's function. It is shown that hybrid GGNRs present the tunable band gap depending upon the width ratio of their components. Modulation of hybrid GGNRs can give rise to the lower thermal conductance of phonons and the better thermoelectric properties compared to pure graphene nanoribbons and graphane nanoribbons. Introducing the hydrogen defects can enhance the maximum of ZT (ZTmax) in both armchair GGNRs (AGGNRs) and zigzag GGNRs (ZGGNRs). Such the enhancement of ZTmax sensitively depends upon the defect concentrations. Among different defect concentrations, ZTmax for the 20 % defect concentration has the highest value, which can be enhanced to 0.42 and 0.24 at T = 300 K in AGGNRs and ZGGNRs, respectively. A laconic analysis of these results is given.

Trapped acoustic waves and raindrops: high-order accurate integral equation method for localized excitation of a periodic staircase

We present a high-order boundary integral equation (BIE) method for the frequency-domain acoustic scattering of a point source by a singly-periodic, infinite, corrugated boundary. We apply it to the accurate numerical study of acoustic radiation in the neighborhood of a sound-hard two-dimensional staircase modeled after the El Castillo pyramid. Such staircases support trapped waves which travel along the surface and decay exponentially away from it. We use the array scanning method (Floquet–Bloch transform) to recover the scattered field as an integral over the family of quasiperiodic solutions parameterized by on-surface wavenumber. Each such BIE solution requires the quasiperiodic Green's function, which we evaluate using an efficient integral representation of lattice sum coefficients. We avoid the singularities and branch cuts present in the array scanning integral by complex contour deformation. For each frequency, this enables a solution accurate to around 10 digits in a few seconds. We propose a residue method to extract the limiting powers carried by trapped modes far from the source. Finally, by computing the trapped mode dispersion relation, we use a simple ray model to explain an acoustic chirp-like time-domain response that is referred to in the literature as the “raindrop effect.”

Enhancing subsurface seismic profiling with distributed acoustic sensing and optimization algorithms

The distribution of shear-wave velocities in the subsurface is generally used to assess the potential for seismic liquefaction and soil amplification effects and to classify seismic sites. Newly developed distributed acoustic sensing (DAS) technology enables estimation of the shear-wave distribution as a high-density seismic observation system. This technology is characterized by low maintenance costs, high-resolution outputs, and real-time data transmission capabilities, albeit with the challenge of managing massive data generation. Rapid and efficient interpretation of data is the key to advancing application of the DAS technology. In this study, field tests were carried out to record ambient noise over a short period using DAS technology, from which the surface-wave dispersion curves were extracted. In order to reduce the influence of directional effects on the results, an unsupervised clustering method is used to select appropriate clusters to extract the Green's function. A combination of a genetic algorithm and Monte Carlo (GA-MC) simulation is proposed to invert the subsurface velocity structure. The stratigraphic profiles obtained by the GA-MC method are in agreement with the borehole profiles. Compared to other methods, the proposed optimization method not only improves the solution quality but also reduces the solution time.

Electron Transport through Linear-, Broken-, and Cross-Conjugated Polycyclic Compounds.

Quantum interference (QI) effects offer unique opportunities to modulate charge transport through single molecules. In recent years, several transmission selection rules have been developed to determine constructive and destructive QIs in an intuitive and simple manner, although some of these rules fail for cross-conjugated systems. In this work, we evaluate the performance of distinct transmission rules on a broad series of anthracene and fluorene derivatives with distinctive structural features including linear-, broken-, and cross-conjugation, heteroatoms, and five-membered rings as such species affords a predictive challenge for the qualitative selection rules for QI effects. The electron transport properties and local transmission plots are first evaluated by combining DFT and the nonequilibrium Green function method allowing for an equal-footing comparison of the conductance of the different polycyclic compounds. Our findings are in line with experimental observations on the influence of the type of conjugation and the connectivity to the metallic electrodes on the transport properties. Thus, cross-conjugated systems exhibit reduced conductance values as compared to the linear-conjugated ones, although the transmission is enhanced in the meta-connected junctions. Remarkably, our study reveals that aromatic cores exhibit generally larger zero-bias conductance for a given connectivity, in contrast to the negative aromaticity-conductance relationship found in literature.

Surface Green's functions for an anisotropic viscoelastic half-plane and their application to contact problems

In this paper, the elastic-like surface Green's functions for an anisotropic viscoelastic half-plane are derived using the time-stepping method. Using the elastic-like surface Green's functions as the core analytical solutions, we develop semi-analytical models (SAMs) and apply them to solve two different contact problems with anisotropic viscoelastic materials. As new modeling approaches, the SAMs developed here can provide fast and efficient approaches to solving contact problems. These methods enable us to consider contact problems with generally anisotropic viscoelastic solids, in which the contact surface is frictional and either smooth or rough, and the applied loads and boundaries can be time-variant. The correctness of the derived surface Green's functions is demonstrated by comparing the numerical results obtained by SAMs and those achieved from the analytical solutions or boundary element methods. Using the obtained numerical results, the impacts of time step size, anisotropy, frictional coefficient, roughness, and applied loads on the contact responses are further analyzed and discussed.

Frequency‐Bessel Transform Method for Multimodal Dispersion Measurement of Surface Waves From Distributed Acoustic Sensing Data

AbstractThe array‐based frequency‐Bessel transform method has been demonstrated to effectively extract dispersion curves of higher‐mode surface waves from the empirical Green's functions (EGFs) of displacement fields reconstructed by ambient noise interferometry. Distributed acoustic sensing (DAS), a novel dense array observation technique, has been widely implemented in surface wave imaging to estimate subsurface velocity structure in practice. However, there is still no clear understanding in theory about how to accurately extract surface‐wave dispersion curves directly from DAS strain (or strain rate) data. To address this, we extend the frequency‐Bessel transform method by deriving Green’s functions (GFs) for horizontal strain fields, making it applicable to DAS data. First, we test its performance using synthetic GFs and verify the correctness of extracted dispersion spectrograms with theoretical results. Then, we apply it to three field DAS ambient‐noise data sets, two recorded on land and one in the seabed. The reliability and advantages of the method are confirmed by comparing results with the widely used phase shift method. The results demonstrate that our extended frequency‐Bessel transform method is reliable and can provide more abundant and higher‐quality dispersion information of surface waves. Moreover, our method is also adaptable for active‐source DAS data with simple modifications to the derived transform formulas. We also find that the gauge length in the DAS system significantly impacts the polarity and value of extracted dispersion energy. Overall, our study provides a theoretical framework and practical tool for multimodal surface wave dispersion measurement using DAS data.

On the vanishing of Green’s function, desingularization and Carleman’s method

The subject of the present paper is the phenomenon of vanishing for the Green function of the operator − Δ + V -\Delta + V on R 3 \mathbb {R}^3 at the points where the potential V V has positive critical singularities. More precisely, under minimal assumptions on V V (i.e., the form-boundedness), an upper bound on the order of vanishing of the Green function is obtained. As a byproduct, the existing results on the strong unique continuation for eigenfunctions of − Δ + V -\Delta +V in dimension d = 3 d=3 are improved.

First-Principles Insights into Highly Sensitive and Reusable MoS2 Monolayers for Heavy Metal Detection.

This study explores the potential of MoS2 monolayers as heavy metal sensors for As, Cd, Hg, and Pb using density functional theory (DFT) and Non-Equilibrium Green's Function (NEGF) simulations. Our findings reveal that As and Pb adsorption significantly alters the surface structure and electronic properties of MoS2, introducing impurity levels and reducing the band gap. Conversely, Cd and Hg exhibit weaker interactions with the MoS2 surface. The MoS2 monolayer sensors demonstrate exceptional sensitivity for all four target heavy metals, with values reaching 126,452.28% for As, 1862.67% for Cd, 427.71% for Hg, and 83,438.90% for Pb. Additionally, the sensors demonstrate selectivity for As and Pb through distinct response peaks at specific bias voltages. As and Pb adsorption also induces magnetism in the MoS2 system, potentially enabling magnetic sensing applications. The MoS2 monolayer's moderate adsorption energy facilitates rapid sensor recovery at room temperature for As, Hg, and Cd. Notably, Pb recovery time can be significantly reduced at elevated temperatures, highlighting the reusability of the sensor. These results underscore the potential of MoS2 monolayers as highly sensitive, selective, and regenerable sensors for real-time heavy metal detection.

On the calculation of irregular solutions of the Schrödinger equation for non-spherical potentials with applications to metallic alloys

The irregular solutions of the stationary Schrödinger equation are important for the fundamental formal development of scattering theory. They are also necessary for the analytical properties of the Green function, which in practice can greatly speed up calculations. Nevertheless, they are seldom considered in numerical treatments because of their divergent behavior at origin. This divergence demands high numerical precision that is difficult to achieve, particularly for non-spherical potentials which lead to different divergence rates in the coupled angular momentum channels. Based on an unconventional treatment of boundary conditions, an integral-equation method is here developed which is capable of dealing with this problem. The available precision is illustrated by electron-density calculations for NiTi in its monoclinic B19’ structure.

Vertical line time domain green function and its applications in numerical simulation of ship seakeeping performance

In present study, a vertical line source time domain Green function is proposed and the subsequent numerical evaluation methods are described in detail. For which, Taylor expansion and Chebyshev approximation algorithms are originally extended from point source to line source for small parameters, as well as asymptotic expansions are extended for large parameters. Meanwhile, polynomials are originally proposed to replace the asymptotic expansions to improve the computational efficiency. The accuracy and stability of the proposed method are validated through several cases and good agreement can be obtained.Furthermore, a hybrid Green function method based on the vertical line source Green function and Rankine source is developed for time domain simulation of seakeeping performances of ships. With respect to the hybrid method, the flow domain is divided into inner part and outer part by an artificial control surface. The first-order Taylor Expansion Boundary Element Method (TEBEM) based on the Rankine panel distribution is applied in the inner part, while three-dimensional panel method based on the vertical line source Green function distribution is adopted in the outer part. Under this circumstance, motions of the single-ship (Slender Wigley and Blunt Wigley) and two-ship (two side-by-side ships) in head waves are numerically investigated. The numerical results agree well with the experimental data, which proved the feasibility and the accuracy of present hybrid Green function method for motion prediction of both single-ship and two-ship.

Density Functional Theory Provides Insights into β-SnSe Monolayers as a Highly Sensitive and Recoverable Ozone Sensing Material.

This study explores the potential of β-SnSe monolayers as a promising material for ozone (O3) sensing using density functional theory (DFT) combined with the non-equilibrium Green's function (NEGF) method. The adsorption characteristics of O3 molecules on the β-SnSe monolayer surface were thoroughly investigated, including adsorption energy, band structure, density of states (DOSs), differential charge density, and Bader charge analysis. Post-adsorption, hybridization energy levels were introduced into the system, leading to a reduced band gap and increased electrical conductivity. A robust charge exchange between O3 and the β-SnSe monolayer was observed, indicative of chemisorption. Recovery time calculations also revealed that the β-SnSe monolayer could be reused after O3 adsorption. The sensitivity of the β-SnSe monolayer to O3 was quantitatively evaluated through current-voltage characteristic simulations, revealing an extraordinary sensitivity of 1817.57% at a bias voltage of 1.2 V. This sensitivity surpasses that of other two-dimensional materials such as graphene oxide. This comprehensive investigation demonstrates the exceptional potential of β-SnSe monolayers as a highly sensitive, recoverable, and environmentally friendly O3 sensing material.

Symmetry constraints and spectral crossing in a Mott insulator with Green's function zeros

Lattice symmetries are central to the characterization of electronic topology. Recently, it was shown that Green's function eigenvectors form a representation of the space group. This formulation has allowed the identification of gapless topological states even when quasiparticles are absent. Here we demonstrate the profundity of the framework in the extreme case, when interactions lead to a Mott insulator, through a solvable model with long-range interactions. We find that both Mott poles and zeros are subject to the symmetry constraints, and relate the symmetry-enforced spectral crossings to degeneracies of the original noninteracting eigenstates. Our results lead to new understandings of topological quantum materials and highlight the utility of interacting Green's functions toward their symmetry-based design. Published by the American Physical Society 2024

Caloric functions and boundary regularity for the fractional Laplacian in Lipschitz open sets

AbstractWe give Martin representation of nonnegative functions caloric with respect to the fractional Laplacian in Lipschitz open sets. The caloric functions are defined in terms of the mean value property for the space-time isotropic $$\alpha $$ α -stable Lévy process. To derive the representation, we first establish the existence of the parabolic Martin kernel. This involves proving new boundary regularity results for both the fractional heat equation and the fractional Poisson equation with Dirichlet exterior conditions. Specifically, we demonstrate that the ratio of the solution and the Green function is Hölder continuous up to the boundary.

Nonequilibrium Green's function approach to low-energy fission dynamics: Fluctuations in fission reactions

Nonequilibrium Green's function approach to low-energy fission dynamics: Fluctuations in fission reactions

Half-Metallic Transport and Spin-Polarized Tunneling through the van der Waals Ferromagnet Fe4GeTe2.

We examine the coherent spin-dependent transport properties of the van der Waals (vdW) ferromagnet Fe4GeTe2 using density functional theory combined with the nonequilibrium Green's function method. Our findings reveal that the conductance perpendicular to the layers is half-metallic, meaning that it is almost entirely spin-polarized. This property persists from the bulk to a single layer, even under significant bias voltages and with spin-orbit coupling. Additionally, using dynamical mean field theory for quantum transport, we demonstrate that electron correlations are important for magnetic properties but minimally impact the conductance, preserving almost perfect spin-polarization. Motivated by these results, we then study the tunnel magnetoresistance (TMR) in a magnetic tunnel junction consisting of two Fe4GeTe2 layers with the vdW gap acting as an insulating barrier. We predict a TMR ratio of ∼500%, which can be further enhanced by increasing the number of Fe4GeTe2 layers in the junction.

Efficient, nonparametric removal of noise and recovery of probability distributions from time series using nonlinear-correlation functions: Photon and photon-counting noise.

A preceding paper [M. Dhar, J. A. Dickinson, and M. A. Berg, J. Chem. Phys. 159, 054110 (2023)] shows how to remove additive noise from an experimental time series, allowing both the equilibrium distribution of the system and its Green's function to be recovered. The approach is based on nonlinear-correlation functions and is fully nonparametric: no initial model of the system or of the noise is needed. However, single-molecule spectroscopy often produces time series with either photon or photon-counting noise. Unlike additive noise, photon noise is signal-size correlated and quantized. Photon counting adds the potential for bias. This paper extends noise-corrected-correlation methods to these cases and tests them on synthetic datasets. Neither signal-size correlation nor quantization is a significant complication. Analysis of the sampling error yields guidelines for the data quality needed to recover the properties of a system with a given complexity. We show that bias in photon-counting data can be corrected, even at the high count rates needed to optimize the time resolution. Using all these results, we discuss the factors that limit the time resolution of single-molecule spectroscopy and the conditions that would be needed to push measurements into the submicrosecond region.

Electron-phonon coupling and magnetic proximity effects on the RKKY interaction in topological crystalline insulators

Understanding the intricacies of magnetism mechanisms on the surface of topological materials, and focusing on the Ruderman-Kittel-Kasuya-Yosida interaction and its modulation, proves to be intriguing for spintronic applications. In this study, we explore switching possibilities between ferromagnetic (FM) and antiferromagnetic (AFM) couplings on the surface of topological crystalline insulator SnTe through electron-phonon coupling (EPC) and magnetic proximity effect (MPE). Our calculations, based on retarded Green's functions in real space, provide insights into the impact of EPC and MPE on FM/AFM couplings at intermediate impurity separations, where significant responses occur. Importantly, both factors induce the switch between FM and AFM in the XYZ-Heisenberg Jx/y/z and in-plane symmetric Jxy components.

Dynamics of proton tunneling in Hydrogen-Bonded systems through Green's function formalism

This study proposes a new theoretical model based on Green's function formalism for studying proton tunneling via hydrogen bonding. This approach allows calculating the tunneling probability and the tunneling energy that proton transfer occurs along a given path inferred a priori. The method is extended to multiple protons tunneling, characterizing the behaviour of some biological molecules. Specifically, the cases of the proton transfer in the Fujicurin A molecule and the double proton tunneling in the Guanine-Cytosine base-pair are investigated. The new approach is an alternative to those present in the literature. It allows straightforwardly predicting the mechanisms of intramolecular and intermolecular proton transfers involving the rearrangement of conjugated electrons.

Geometric Amplitude Accompanying Local Responses: Spinor Phase Information from the Amplitudes of Spin-Polarized STM Measurements.

Solving the Hamiltonian of a system yields the energy dispersion and eigenstates. The geometric phase of the eigenstates generates many novel effects and potential applications. However, the geometric properties of the energy dispersion go unheeded. Here, we provide geometric insight into energy dispersion and introduce a geometric amplitude, namely, the geometric density of states (GDOS) determined by the Riemann curvature of the constant-energy contour. The geometric amplitude should accompany various local responses, which are generally formulated by the real-space Green's function. Under the stationary phase approximation, the GDOS simplifies the Green's function into its ultimate form. In particular, the amplitude factor embodies the spinor phase information of the eigenstates, favoring the extraction of the spin texture for topological surface states under an in-plane magnetic field through spin-polarized STM measurements. This work opens a new avenue for exploring the geometric properties of electronic structures and excavates the unexplored potential of spin-polarized STM measurements to probe the spinor phase information of eigenstates from their amplitudes.