Green Function Research Articles

Time‐Resolved Optical Response of the Dicke's Model via the Nonequilibrium Green's Function Approach

Due to their conceptual appeal and computational convenience, two‐level systems (TLSs) and generalizations are used to investigate nonlinear behavior in quantum optics and assess the applicability of theoretical methods. Herein, the focus is on second‐harmonic generation (SHG) and, as system of interest, on the Dicke model, which consists of several TLSs inside an optical cavity. The main aspect addressed is the scope of nonequilibrium Green's function (NEGF) to describe the effect of inhomogeneities and electron–electron (e–e) interactions on the SHG signal. For benchmarking purposes, exact diagonalization (ED) results are also presented and discussed. SHG spectra obtained with NEGF and ED are found to be in very good mutual agreement in most situations. Furthermore, inhomogeneity in the TLS and e–e interactions reduce the SHG signal, and the reduction is stronger with inhomogeneity than with interactions. This trend is consistently noted across different (small to large) system sizes. Finally, a modified NEGF approach is proposed to account for cavity leakage, where the quantum photon fields are coupled to a bath of classical oscillators. As expected, within this mixed quantum‐classical scheme, a decrease in the intensity of the fluorescent spectra takes place depending on the entity of leakage.

Modeling oxygen transport in the brain: An efficient coarse-grid approach to capture perivascular gradients in the parenchyma.

Recent progresses in intravital imaging have enabled highly-resolved measurements of periarteriolar oxygen gradients (POGs) within the brain parenchyma. POGs are increasingly used as proxies to estimate the local baseline oxygen consumption, which is a hallmark of cell activity. However, the oxygen profile around a given arteriole arises from an interplay between oxygen consumption and delivery, not only by this arteriole but also by distant capillaries. Integrating such interactions across scales while accounting for the complex architecture of the microvascular network remains a challenge from a modelling perspective. This limits our ability to interpret the experimental oxygen maps and constitutes a key bottleneck toward the inverse determination of metabolic rates of oxygen. We revisit the problem of parenchymal oxygen transport and metabolism and introduce a simple, conservative, accurate and scalable direct numerical method going beyond canonical Krogh-type models and their associated geometrical simplifications. We focus on a two-dimensional formulation, and introduce the concepts needed to combine an operator-splitting and a Green's function approach. Oxygen concentration is decomposed into a slowly-varying contribution, discretized by Finite Volumes over a coarse cartesian grid, and a rapidly-varying contribution, approximated analytically in grid-cells surrounding each vessel. Starting with simple test cases, we thoroughly analyze the resulting errors by comparison with highly-resolved simulations of the original transport problem, showing considerable improvement of the computational-cost/accuracy balance compared to previous work. We then demonstrate the model ability to flexibly generate synthetic data reproducing the spatial dynamics of oxygen in the brain parenchyma, with sub-grid resolution. Based on these synthetic data, we show that capillaries distant from the arteriole cannot be overlooked when interpreting POGs, thus reconciling recent measurements of POGs across cortical layers with the fundamental idea that variations of vascular density within the depth of the cortex may reveal underlying differences in neuronal organization and metabolic load.

Spin-Orbit Torque in Single-Molecule Junctions from ab Initio.

The use of electric fields applied across magnetic heterojunctions that lack spatial inversion symmetry has been previously proposed as a nonmagnetic means of controlling localized magnetic moments through spin-orbit torques (SOT). The implementation of this concept at the single-molecule level has remained a challenge, however. Here, we present first-principles calculations of SOT in a single-molecule junction under bias and beyond linear response. Employing a self-consistency scheme invoking density functional theory and nonequilibrium Green's function theory including spin-orbit interaction, we compute the change of the magnetization with the bias voltage and the associated current-induced SOT. Within the linear regime our quantitative estimates for the SOT in single-molecule junctions yield values similar to those known for magnetic interfaces. Our findings contribute to an improved microscopic understanding of SOT in single molecules.

Electronic Couplings and Conversion Dynamics between Localized and Charge Transfer Excitations from Many-Body Green's Functions Theory.

We investigate the determination of electronic coupling between localized excitations (LEs) and charge-transfer (CT) excitations based on many-body Green's functions theory in the GW approximation with the Bethe-Salpeter equation (GW-BSE). Using a small molecule dimer system, we first study the influence of different diabatization methods, as well as different model choices within GW-BSE, such as the self-energy models or different levels of self-consistency, and find that these choices affect the LE-CT couplings only minimally. We then consider a large-scale low-donor morphology formed from rubrene and fullerene and evaluate the LE-CT couplings based on coupled GW-BSE-molecular mechanics calculations. For these disordered systems of bulky molecules, we observe differences in the couplings based on the Edmiston-Ruedenberg diabatization compared to the more approximate Generalize Mulliken-Hush and fragment charge difference diabatization formalisms. In a kinetic model for the conversion between LE and CT states, these differences affect the details of state populations in an intermediate time scale but not the final populations.

Molecular heat transport across a time-periodic temperature gradient.

The time-periodic modulation of a temperature gradient can alter the heat transport properties of a physical system. Oscillating thermal gradients give rise to behaviors such as modified thermal conductivity and controllable time-delayed energy storage that are not present in a system with static temperatures. Here, we examine how the heat transport properties of a molecular lattice model are affected by an oscillating temperature gradient. We use analytical analysis and molecular dynamics simulations to investigate the vibrational heat flow in a molecular lattice system consisting of a chain of particles connected to two heat baths at different temperatures, where the temperature difference between baths is oscillating in time. We derive expressions for heat currents in this system using a stochastic energetics framework and a nonequilibrium Green's function approach that is modified to treat the nonstationary average energy fluxes. We find that emergent energy storage, energy release, and thermal conductance mechanisms induced by the temperature oscillations can be controlled by varying the frequency, waveform, and amplitude of the oscillating gradient. The developed theoretical approach provides a general framework to describe how vibrational heat transmission through a molecular lattice is affected by temperature gradient oscillations.

Carrier Transport Properties of the Orthorhombic Phase Boron Nitride Nanoribbons and Rectifying Device Design

Using density functional theory combined with nonequilibrium Green's function, the electronic structures and carrier transport properties of the orthorhombic phase boron nitride nanoribbons (BNNRs) with different edges and different widths are investigated. The calculated results show that both armchair‐ and zigzag‐edged BNNRs are direct bandgap semiconductors. The quantum confinement gives rise to a distinct bandgap for the 1D BNNRs, and the edged atoms play an important role on their electronic structures. The bandgaps of the armchair‐edged BNNRs approach 0.5–0.8 eV when their widths are sufficiently large. However, the electronic structures of the zigzag‐edged BNNRs exhibit more variations dependent on their edged atoms. The J–V characteristics of the BNNRs reveal that the zigzag‐edged BNNRs have superior J–V performance to that of the armchair‐edged counterparts. Eventually, a computational nanodevice design is proposed to achieve rectifying behavior by constructing an in‐plane heterojunction based on the BNNRs without any doping, and the left and right electrodes are formed by differently edged atoms and a small strain is performed on the left electrode. The rectification ratio of about 77.36 is realized. The findings provide comprehensive understandings of the orthorhombic BN monolayer, which can be helpful to its potential application for nanoelectronics.

Quantum Algorithm for Imaginary-Time Green's Functions.

Green's function methods lead to ab initio, systematically improvable simulations of molecules and materials while providing access to multiple experimentally observable properties such as the density of states and the spectral function. The calculation of the exact one-particle Green's function remains a significant challenge for classical computers and was attempted only on very small systems. Here, we present a hybrid quantum-classical algorithm to calculate the imaginary-time one-particle Green's function. The proposed algorithm combines the variational quantum eigensolver and the quantum subspace expansion methods to calculate Green's function in Lehmann's representation. We demonstrate the validity of this algorithm by simulating H2 and H4 on quantum simulators and on IBM's quantum devices.

Generalizations of Levinson-type inequalities via new Green functions and Hermite interpolating polynomial

In this study, Levinson-type inequalities for the class of n-convex (n≥3\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$n \\geq 3$\\end{document}) functions are generalized using new Green functions and the Hermite interpolating polynomial involving two types of data points. Some estimations for novel functionals are derived using f-divergence. Furthermore, different inequalities involving Shannon entropies are presented.

Dirac walks on regular trees

Abstract The study of matter fields on an ensemble of random geometries is a difficult problem still in need of new methods and ideas. 
We will follow a point of view inspired by probability theory techniques that relies on an expansion of the two point function as a sum over random walks.
An analogous expansion for Fermions on non-Euclidean geometries is still lacking. Casiday et al. [Laplace and Dirac operators on
graphs , Linear and Multilinear Algebra (2022) 1] proposed a classical “Dirac walk” diffusing on vertices and edges of an oriented graph with a square root of the graph Laplacian. In contrast to the simple random walk, each step of the walk is given a sign depending on the orientation of the edge it goes through. In a toy model, we propose here to study the Green functions, spectrum and the spectral dimension of such “Dirac walks” on the Bethe lattice, a d-regular tree. The recursive structure of the graph makes the problem exactly solvable. Notably, we find that the spectrum develops a gap and that the spectral dimension of the Dirac walk matches that of the simple random walk (ds=1 for d=2 and ds=3 for d ≧3).

Exact Functional Integration of Radial and Complex Slave‐Boson Fields: Thermodynamics and Dynamics of the Two‐Site Extended Hubbard Model

AbstractThe functional integral formulation of the Hubbard model when treated in its Kotliar‐Ruckenstein representation in the radial gauge involves fermionic, as well as complex and radial slave boson fields. In order to improve on the understanding of the interplay of the three types of fields, and on the nature of the latter, a comprehensive investigation of an exactly solvable two‐site cluster is performed, as it entails all pitfalls embodied in this approach. It is first shown that the exact partition function is recovered, even when incorporating in the calculation the square root factors that are at the heart of the representation, when suitably regularized. It is shown that using radial slave boson fields allows to overcome all hurdles following from the normal ordering procedure. It is then demonstrated that this applies to the Green's function as well, and to the correlation functions of physical interest, thereby answering the criticisms raised by Schönhammer [K. Schönhammer, Phys. Rev. B 1990 42, 2591]. In addition, the investigation generalizes the calculations to the Hubbard model extended by a non‐local Coulomb interaction.

Environmental Dyeing and Functionalization of Silk Fabrics with Natural Dye Extracted from Lac.

Most traditional synthetic dyes and functional reagents used in silk fabrics are not biodegradable and lack green environmental protection. Natural dyes have attracted more and more attention because of their coloring, functionalization effects, and environmental benefits. In this study, natural dyes were extracted from lac and used for coloring and functionalization in silk fabrics without any other harmful dyes. The extraction conditions were studied and analyzed by the univariate method. The optimal extraction process was that the volume ratio of ethanol to water was 60:40 with a solid-liquid ratio of 1:10, and reacting under the neutrality condition for 1 h at 70 °C. Silk fabric can be dyed dark owing to the certain lifting property of lac. After being dyed by Al3+ post-medium, the levels of the washing fastness, light fastness, and friction fastness of silk fabric are all above four with excellent fastness. The results show that the dyed silk fabrics have good UV protection, antioxidation, and antibacterial properties. The UV protection coefficient UPF is 42.68, the antioxidant property is 98.57%, and the antibacterial property can reach more than 80%. Therefore, the dyeing and functionalization of silk fabrics by utilizing naturally lac dyes show broad prospects in terms of the application of green sustainable dyeing and functionalization.

DC electric field assisted heat extraction evaluation via water circulation in abandoned production well patterns: semi-analytical and numerical models

Geothermal energy, recognized for its clean and vast developmental potential, finds untapped promise in many oil fields developed through water injection. However, challenges such as the high costs associated with drilling and development, the expansion of water-clay expansion, and low rock permeability have constrained the broader exploitation of geothermal resources. Here, to address these challenges and harness low-permeability geothermal energy from abandoned wells, this work introduces a novel approach: DC-assisted circulation water injection technology. This study employs the Green function, Newman product, and boundary element methods to develop semi-analytical and numerical models, incorporating a DC electric field to simulate the optimization effect of this field on heat extraction. This work evaluates and optimize the lifetime and economic effects of abandoned wells using the Non Sorting Genetic Algorithm II. Results show that the semi-analytical model monitors the reservoir temperature parameter to optimize the timing for circulation water injection. Additionally, our numerical model demonstrates that, over a span of 5,000 days, a network of wells could generate a revenue of $9.158 million. In summary, DC-assisted abandoned wells to develop geothermal reservoirs is not only feasible but also enhances reservoir permeability and porosity through an electrical conductivity effect, significantly improving heat energy recovery.

Inverse problems for discrete Sturm–Liouville operator having Bessel-type potential

In this paper, inverse problems are studied for Sturm–Liouville difference operators having p 2 − 1 / 4 m 2 type singularity. First, we define the Green's function and the corresponding Weyl function, some of their properties are investigated, and we give a method to find the potential function. Then we give the solution of the inverse nodal problem and present a constructive procedure for the solution of the inverse problem by using nodes.

A novel semi-analytical model for laterally loaded piles

A new model for laterally loaded piles is proposed, consisting of a linear part and a non-linear iterative part. The linear part is based on the Green's function method, which strictly satisfies the displacement and stress continuity conditions at the pile-soil interface and leads to a rigorous solution. The non-linear iterative part assumes that the shear modulus of the soil around the pile decreases with the average strain of the soil layer. Only two soil parameters need to be calibrated, including the initial shear modulus of the soil and the reference shear strain at half the initial modulus. Compared to the finite element model, the advantage of this model is that it converges quickly while maintaining accuracy, which greatly improves computational efficiency. The advantage of this model over the p-y curve model is that it does not have the difficulty of selecting p-y spring parameters, especially for monopiles. The accuracy of this model is verified by comparison with three-dimensional finite element models and nine existing studies, including numerical models, field tests and centrifuge tests. These cases cover various piles with diameters of D∼0.273–10 m and aspect ratios of L/D∼3–40, installed in sand or clay by driving, jacking or vibration.

Tsunami waveform inversion using Green’s functions with advection effects: application to the 2003 Tokachi–Oki earthquake

We explored nonlinear effects within the context of tsunami waveform inversion, wherein Green's functions were linearly superimposed to estimate earthquake slips. We focused on these effects while developing a source model for the 2003 Tokachi–Oki earthquake off Hokkaido, Japan. A source model for this earthquake was developed based on linear tsunami waveform inversion using Green’s functions and tsunami waveforms observed at tide gauge stations. Subsequently, tsunami waveforms from the source were simulated at the stations using nonlinear long-wave theory and compared with those estimated by inversion. The comparisons demonstrated that the waveforms had a non-negligible discrepancy that was attributed to advection effects, even for the primary wave used in the inversion at the two stations. This result strongly suggests that advection effects should be considered in the source modeling of the 2003 earthquake based on tsunami waveforms observed by tide gauges. Based on these results, a new tsunami waveform inversion technique that incorporates linearly approximated advection effects and maintain the framework of linear tsunami waveform inversion using Green’s functions is proposed and applied. The proposed method successfully mimicked the advection effects during the 2003 tsunami, reproduced better tsunami waveforms, and developed a source model for the 2003 earthquake using these effects. The peak slip amount and seismic moment were greater in the source model with advection effects than those without the effects. This finding suggests that the values in the source models developed for other earthquake events without considering these effects may have been underestimated.Graphical abstract

Comment on “Fast and accurate electromagnetic field calculation for substrate-supported metasurfaces using the discrete dipole approximation”

Abstract The article entitled “Fast and accurate electromagnetic field calculation for substrate-supported metasurfaces using the discrete dipole approximation (DDA)” written by W. Liu and E. McLeod presents a method for computing the Green function in presence of a substrate or multilayer in an efficient way. Unfortunately, the proposed method has been known for more than twenty years and significantly ameliorated. It can be found in its optimized version in some open-source DDA codes. In this comment, we recall the different approaches (and related papers) addressing the computation of the Green function of a multilayered system. We show that they address all the points raised by Liu and McLeod in their paper and provide more efficient solutions to their computational issues.

The enhancement of infrared characterization of passivated InAs nanowires

Indium arsenide (InAs) nanowires (NWs) show significant advantages in optoelectronic devices due to their excellent electronic and optical properties. While the surface states affect such outstanding properties, and the performance of optoelectronic devices can be further optimized by modulating the surface state. Herein, the adsorption and substitution properties and the optoelectronics response of passivated InAs NWs are studied using first-principles calculations combined with nonequilibrium Green's function (NEGF). The results show that O atom adsorption can reduce the band gap and improve infrared absorption of InAs NWs. Meanwhile, for the O atom substitution model, the impurity energy level appears near the Fermi level of InAs NWs, and for a higher concentration O atoms substitution, the semiconduction properties of the InAs NWs are destroyed. We also choose the Au, Cs, Bi, Sn, and Y atoms as decoration atoms to passivate InAs NWs, and compared with the intrinsic InAs NW surface model, the energy bands gap of the metal-atoms adsorption models all show a decreasing trend in addition to Au-atom adsorption, and the absorption coefficients of InAs NWs adsorbed by several atoms such as Cs, Sn, Bi, and Y in the infrared region have redshifts in different degrees. The absorption coefficients of InAs NWs adsorbed by several metal atoms, Sn, Bi, and Y, are higher in the infrared region compared to that of InAs NW adsorbed by O atom. After the screening of materials, we select InAs NWs adsorbed with Cs, Bi, Sn, and Y atoms with good infrared absorption characteristics for the performance study of optoelectronic devices and it is shown that the InAs NW devices with adsorbed Bi and Sn atoms have the optimal performance with low dark current and high photocurrent.

Bounds of some divergence measures using Green’s function and Fink’s identity via Diamond Integrals

Abstract In the present paper, some inequalities regarding Csiszár divergence are generalized for diamond integrals by utilizing Green function and Fink’s identity. By selecting various kinds of convex functions, bound of different entropies and divergence measures are obtained. Furthermore, in seek of applications, bounds of different divergence measures are estimated on diverse fixed time scales. These divergence measures are fundamental in problems pertaining to source and channel coding, large deviations theory, and other sorts of problems.

Formal Green's function theory in non-Hermitian lattice systems

Formal Green's function theory in non-Hermitian lattice systems

Effect of soil layering and interface resistance on electro‐osmotic consolidation of layered soils: A Green's function approach

AbstractDuring electro‐osmotic consolidation, effective voltage attenuation induced by the increasing interface resistance is an important phenomenon, which significantly decreases consolidation effectiveness. This paper presents an analytical model for one‐dimensional electro‐osmotic consolidation in layered soils with horizontal graphite electrodes considering effective voltage attenuation. The mathematical model is characterized by time‐dependent source term and discontinuous interface flux. New variables are introduced to homogenize the discontinuous interface flux and Green’s function method is used to solve the new nonhomogeneous governing equations with nonhomogeneous boundaries. Several verification examples are conducted using the existing analytical solution and numerical results. Parametric studies indicate that electro‐osmotic consolidation of layered soils cannot be accurately simulated by equivalent homogeneous soil, whether effective voltage attenuation is considered or not. Furthermore, the backflow phenomenon may occur due to effective voltage attenuation, while it may disappear when the anode is placed in the low‐permeability layer. In addition, the optimal arrangement of electrodes in layered soils is also investigated. When the ratio of the thickness of low‐permeability layer to high‐permeability layer is about 1/3, installing the cathode in the low‐permeability layer can improve the electro‐osmosis effect up to two times, compared with installing the anode in the low‐permeability layer.