Green Function Research Articles

The free-space dyadic Green function is orthogonal to its curl

The free-space dyadic Green function in electromagnetics is orthogonal to its own curl on any spherical surface whose center is the source point.

Out-of-time-ordered correlators in the IP matrix model

We study the out-of-time-ordered correlators (OTOCs) in the IP matrix model [1]. It was shown in [2] that OTOCs do not grow when the adjoint is massless. We generalize the analysis of OTOCs to general nonzero masses m > 0 for the adjoint, where we give a new prescription for analytic continuation in time such that we can evaluate OTOCs numerically using the retarded Green function. Despite the fact that the behaviors of the two-point functions, spectral density, and the Krylov complexity change drastically depending on whether the adjoint is massless or not, in the parameter ranges we study, we do not see the exponential growth of OTOCs for the massive adjoint cases. We end with a discussion of the comparison of this model with the SYK model and possible modification of the model.

Microscopic Green's function approach for generalized Dirac Hamiltonians

Microscopic Green's function approach for generalized Dirac Hamiltonians

Three-dimensional Effects on Gap-Resonances in Twin-Hull Vessels in Time-Harmonic Vertical Oscillations

Three-dimensional effects induced by dimensional ratios on the gap resonances happening in twin hull vessels oscillating in forced vertical motion have been analyzed. They can lead to relevant consequences, such as the amplification of the inner radiated waves or the generation of standing waves in between the demi-hulls, that can have a direct effect on the operating profile of the vessel. The response of twin hull vessels in waves can be strongly affected by these resonant phenomena. Also, some of these behaviors can be exploited in the framework of wave energy conversion systems. The present analysis is carried out by using an open-source, linear, Boundary Element Method (BEM), based on the Green function approach. Mathematical backgrounds of the added mass and damping coefficients computation for a floating body under harmonic vertical oscillation are provided as well as details of the numerical discretization used in the BEM. A panel mesh sensitivity study is carried out and the numerical prediction is validated by comparison against available experimental data, another CFD solution obtained by a high-fidelity viscous solver based on the open-source libraries Open-FOAM and approximate analytic formulations. The effect of the beam ratio and the length-to-beam ratio on the resonant phenomena has been analyzed. This has been achieved by systematic variations of the geometric dimensions of the hull, focusing on the trends of the hydrodynamic coefficients, the amplitude of the radiated waves, and the location of the resonant frequencies over the analyzed range.

NG-DPSM: A neural green-distributed point source method for modelling ultrasonic field emission near fluid-solid interface using physics informed neural network

Distributed point source method (DPSM) is a collocation point-based semi-analytical method to model the scattered ultrasonic fields in isotropic and anisotropic materials. It requires the evaluation of Green's function solutions and its rigorous differentiation for complex geometry problems having a large set of distributed point sources. DPSM is much faster than the finite element method (FEM) however, it is analytically demanding as it requires differentiation of the Green's function. The intricacy associated with differentiation operation hinders the potential application of DPSM in large-scale automation and real-time structural health monitoring. The current paper introduces machine-learning-based strategies within DPSM and yields the proposed Neural Green-DPSM (NG-DPSM) framework. A physics-informed neural network (PINN) is incorporated in the DPSM framework for evaluating the Green's function and its gradients. To train the PINN, displacement Green's function solutions of wave propagation in isotropic solid is used as the governing physics. Once the PINN is trained for displacement Green's function solutions, the NG-DPSM framework leverages the trained network and its automatic differentiation capability to predict displacement and stress fields annihilating the rigorous differentiation of Green's functions. The accuracy and efficacy of NG-DPSM are demonstrated using two numerical experiments. First, the ultrasonic fields are evaluated for the problem geometry of a plate immersed in fluid excited at different angles of incidence. Further, the efficacy of the proposed approach is demonstrated for wave scattering through a circular hole in the plate. The results show a strong agreement between the ultrasonic fields computed using both NG-DPSM and conventional DPSM.

First-Principles Simulation and Materials Screening for Spin-Orbit Torque in 2D van der Waals Heterostructures.

Recent advancements in spin-orbit torque (SOT) technology in two-dimensional van der Waals (2D vdW) materials have not only pushed spintronic devices to their atomic limits but have also unveiled unconventional torques and novel spin-switching mechanisms. The vast diversity of SOT observed in numerous 2D vdW materials necessitates a screening strategy to identify optimal materials for torque device performance. However, such a strategy has yet to be established. To address this critical issue, a combination of density functional theory and non-equilibrium Green's function is employed to calculate the SOT in various 2D vdW bilayer heterostructures. This leads to the discovery of three high SOT systems: WTe2/CrSe2, MoTe2/VS2, and NbSe2/CrSe2. Furthermore, a figure of merit that allows for rapid and efficient estimation of SOT is proposed, enabling high-throughput screening of optimal materials and devices for SOT applications in the future.

Study of Carbon monoxide adsorption on B-N doped hydrogenated Sn nanoribbons towards nanosensor applications

This study utilized Van der Waals corrected density functional theory (DFT) and nonequilibrium Green's function (NEGF) to consider the potential of hydrogenated Armchair stanene nanoribbons of width 8 (HASnNR(8)) for CO gas detection. The study analyzed the most stable adsorption configuration, charge transfer, electronic transport, adsorption energy, sensitivity and electronic properties of CO gas molecules on HASnNR(8), both before and after B-N doping. The results showed that B-N doping led to a significant increase in adsorption energy and a gap opening at the Gamma point, resulting in semiconductor behavior. Analysis of charge transfer indicated that CO molecules acted as donors to HASnNR(8). Moreover, there was a notable change in the transmission functions of CO adsorbed on B-N doped HASnNR(8) compared to pure HASnNR(8). Based on the I-V characteristics, the study concluded that CO molecules could be easily detected after B-N doping. Finally, the study performed a recovery time analysis and sensitivity CO adsorbed on bare and B-N doped HASnNR(8) surfaces, with the results indicating that B-N doped HASnNR is a promising material for CO molecule sensing applications.

Biaxila strain modulated high anisotropic gas-sensing performance of C5N-based two-dimensional devices: A first-principles study

Two-dimensional carbon nitride materials have been widely used in many applications such as device fabrication, gas adsorption and separation due to their abundant element resources, high physicochemical stability and excellent electronic properties. In this paper, density functional theory and non-equilibrium Green's function method are used to study the electronic structure, transport characteristics and gas sensitivity of C5N-based structures. The results show that the electron transport exhibits obvious anisotropy, in which the electron transport in the armchair direction is more conductive than that in the zigzag direction. It is worth noting that the negative differential resistance effect exists in both directions. Furthermore, the transport and sensing characteristics of inorganic molecules (NO, CO, NO2, SO2, and NH3) adsorbed on the C5N monolayer are studied. The results show that CO, SO2 and NH3 exist on the surface of C5N in the form of physical adsorption, while NO and NO2 adhere to the surface of C5N in the form of chemical adsorption. The designed C5N gas sensor exhibits high sensitivity to NO and NO2 molecules, reaching 81 % sensitivity to NO2 at a 0.1 V bias voltage. Finally, the effect of strain on the adsorption properties of gas sensing devices is studied. Studies have shown that the application of -4 % strain in the armchair direction significantly increases the current of NO and NO2, significantly improving the performance of the gas sensor. Whether strain is applied to the device or gas adsorption, C5N materials always maintain significant anisotropy. This study shows that C5N is a highly anisotropic and sensitive two-dimensional material, which has broad application potential in the field of electronic properties and gas sensing.

Effect of static compression on near-field tsunami waves: Three-dimensional solution

An analytical solution of three-dimensional surface wave profiles due to arbitrary spatio-temporal disturbance of a circular ocean bottom in a compressible ocean is obtained by incorporating the influence of the static ocean background compression under the assumptions of linearized water wave theory. Time-domain simulations of the surface profile in three dimensions and the pressure distribution within the water column for a circular uniform rise and tilt are shown. The corresponding animation movies depict the temporal evolution of the surface profile and pressure field inside the water column eloquently, which was not shown in earlier literature. The impact of static compression is also discussed through the simulations. A novel analytical expression of the potential function for a generic tilted motion (rmcos(mθ),m∈Z) of the circular ocean floor is derived. An efficient numerical code is developed to find surface elevation and pressure distribution, implementing the inverse Fourier integral as matrix multiplication. Validation is performed for the specific case of a rising flat ocean floor, showing the oscillations due to acoustic-gravity modes. Initially, a simplified problem of a flat rising ocean bottom is solved using the eigenfunction matching method, which involves finding a particular solution for the nonhomogeneous ocean bottom condition and the solution for its homogeneous counterpart. Solutions are obtained using a newly developed inner product between the depth-dependent functions. Later, a Green function technique is used to incorporate the impact of the arbitrary spatio-temporal motion of the circular portion of the ocean bed. The solution obtained from the eigenfunction matching method is utilised to obtain the analytical form of Green’s function and, eventually, an expression of surface elevation and pressure distribution inside the ocean water column.

The time‐asymptotic expansion for the compressible Euler equations with damping

AbstractIn 1992, Hsiao and Liu first showed that the solution to the compressible Euler equations with damping time‐asymptotically converges to the diffusion wave of the porous media equation. Geng et al. proposed a time‐asymptotic expansion around the diffusion wave , which is a better asymptotic profile than . In this paper, we rigorously justify the time‐asymptotic expansion by the approximate Green function method and the energy estimates. Moreover, the large time behavior of the solution to compressible Euler equations with damping is accurately characterized by the time‐asymptotic expansion.

Elastic and inelastic phonon scattering effects on thermal conductance across Au/graphene/Au interface

Heat dissipation from graphene devices is predominantly limited by heat conduction across the metal contacts with complex phonon scattering. In this work, the effects of elastic and inelastic phonon scattering on the interfacial thermal conductance (ITC) across the Au/graphene/Au interface are studied using both atomistic Green's function (AGF) and reverse non-equilibrium molecular dynamics methods. The results show that the contribution of inelastic phonon scattering to the ITC increases with the enhancement of interfacial bonding strength. Moreover, the overlap of the vibrational density of states across the interface shows that the coupling between the Au layer (adjacent to the Au/graphene interface) and graphene's out-of-plane modes plays the dominant role in ITC across the Au/graphene interface. By comparing the transmission functions calculated with AGF and spectral heat current decomposition methods, the inelastic phonon scattering process facilitates phonon transmission in the lower and higher frequency range but hinders phonon transmission in the intermediate frequency range. It is expected that this study can contribute to a better understanding of the thermal conduction mechanism across the metal/graphene interface, providing guidance for thermal management and heat conduction optimization of graphene in microelectronic devices.

Transition Metal (Co, V, W, Zr) Single-Atom Decorated Biphenylene for Enhancing the Sensing Performance of SF6 Decomposition Molecules.

The highly sensitive gas sensors used to monitor the decomposition of toxic gases in the dielectric materials of electrical equipment are vital in preventing safety problems arising from corrosion of the equipment. Recently, biphenylene (BPN) has been prepared through surface interpolymer hydrofluorination (HF zipper) reaction, whereas potential gas-sensitive devices based on the BPN monolayer have lacked in-depth investigation. The stable geometries, adsorption energies, interlayer distances, and charge transfers of small molecules of toxic gases (H2S, SO2, SOF2, SO2F2) produced by SF6 chalcogenide molecules of decomposition adsorbed on the original BPN monolayer are systematically researched by using nonequilibrium Green's function methods and density functional theory. The results indicated that all small molecules adsorbed on the BPN monolayer are physisorbed, while the type of adsorption turned from physisorption to chemisorption when BPN carried out adsorption with adsorbing a transition metal atom (TMA). In addition, the characteristics of current-voltage (I-V) curves of H2S and SO2 based on the TMA-BPN gas sensors revealed that the currents in BPN-based gas sensors displayed an obvious anisotropy, and the currents in the zigzag direction are larger than that in the armchair orientation regardless of the molecular adsorption cases. Moreover, the difference of currents for TMA-decorated BPN sensors changed more remarkably before and after the adsorption of H2S and SO2 in the zigzag direction. This work offers insights into the design of gas-sensitive devices through the adsorption of small molecules on the TMA-decorated BPN monolayer.

Difference in ship response in waves between strip and 3D methods based on integrated formulation

Numerous benchmark calculations have been performed on ship motions and loads in waves. However, there are usually significant differences between codes, even for programs based on the same theory, and it is often extremely difficult to identify the factors that cause such differences. In this paper, the authors present a formulation of the strip method and 3D method in such a way that the common parts between the two are emphasized, and then develop an integrated program that can handle the two methods (STFM and zero-speed Green's function method) based on this formulation. This approach enables the extraction of the differences in the ship response between the two methods caused by the pure difference in the hydrodynamic force of them, i.e., the 3D effect. A comparison using tank tests under a wide range of conditions is performed to clarify the estimation accuracy of the two methods and the tendency of the 3D effect for ship motion, hull-girder sectional force, and hydrodynamic pressure for a container ship and a VLCC.

Accelerating Nonequilibrium Green Functions Simulations: The G1–G2 Scheme and Beyond

The theory of nonequilibrium Green functions (NEGF) has seen a rapid development over the recent three decades. Applications include diverse correlated many‐body systems in and out of equilibrium. Very good agreement with experiments and available exact theoretical results could be demonstrated if the proper selfenergy approximations were used. However, full two‐time NEGF simulations are computationally costly, as they suffer from a cubic scaling of the computation time with the simulation duration. Recently the G1–G2 scheme that exactly reformulates the generalized Kadanoff–Baym ansatz with Hartree–Fock propagators (HF‐GKBA) into time‐local equations is introduced, which achieves time‐linear scaling and allows for a dramatic speedup and extension of the simulations (Schluenzen et al. Phys. Rev. Lett. 2020, 124, 076601). Remarkably, this scaling is achieved quickly, and also for high‐level selfenergies, including the nonequilibrium GW and T‐matrix approximations (Joost et al. Phys. Rev. B 2020, 101, 245101). Even the dynamically screened ladder approximation is now feasible (Joost et al. Phys. Rev. B 2022, 105, 165155), and also applications to electron‐boson systems are demonstrated. Herein, an overview on recent results that are achieved with the G1–G2 scheme is presented. Problems and open questions are discussed and further ideas of how to overcome the current limitations of the scheme and present are presented. The G1–G2 scheme is illustrated by presenting applying it to the excitation dynamics of Hubbard clusters, to optical excitation of graphene, and to charge transfer during stopping of ions by correlated materials.

Three‐Dimensional Teleseismic Elastic Reverse‐Time Migration With Deconvolution Imaging Condition and Its Application to Southwest Japan

AbstractWe have developed a novel deconvolution‐based reverse time migration method to image lithospheric structures using teleseismic data recorded by dense seismic arrays. Unlike traditional approaches that rely on the retrieval of Green's functions (or receiver functions), the new method directly utilizes the recorded three‐component (3‐C) seismic waveforms to reconstruct subsurface wavefields, which has the advantage of avoiding the estimation and removal of source time function. Importantly, it enables the asymptotic estimation of P‐to‐S transmission conversion coefficients at the elastic discontinuities and enhances resolving power for the fine‐scale heterogeneities. Taking these improvements, we have obtained a full three‐dimensional (3‐D) high‐resolution image of the subduction zone beneath southwest Japan. This image provides a comprehensive configuration of the severely deformed subducting plate beneath the Kii Channel and Kinki Peninsula.

Floquet non-equilibrium Green's function and Floquet quantum master equation for electronic transport: The role of electron-electron interactions and spin current with circular light.

The non-equilibrium Green's function (NEGF) and quantum master equation (QME) are two main classes of approaches for electronic transport. We discuss various Floquet variances of these formalisms for transport properties of a quantum dot driven via interaction with an external periodic field. We first derived two versions of the Floquet NEGF. We also explore an ansatz of the Floquet NEGF formalism for the interacting systems. In addition, we derived two versions of Floquet QME in the weak interaction regime. With each method, we elaborate on the evaluation of the expectation values of the number and current operators. We examined these methods for transport through a two-level system that is subject to periodic driving. The numerical results of all four methods show good agreement for non-interacting systems in the weak regime. Furthermore, we have observed that circular light can introduce spin current. We expect these Floquet quantum transport methods to be useful in studying molecular junctions exposed to light.

Exploring Intertwined Quantum and Cryogenic Behaviour in Ultra-Scaled 10nm MOSFET: A NEGF Quantum Ballistic Simulation

Abstract Silicon-based spin qubits have emerged as promising candidates for scalable quantum information processing. This study first time investigates the behaviour of ultra-scaled 10nm gate length and 3nm channel thickness nanoscale double gate metal-oxide semiconductor field-effect transistors (MOSFETs) over a broad temperature range, from deep cryogenic (4 K) to room temperature (300 K). Employing the Non-Equilibrium Green's Function (NEGF) method, the research explores the intertwined quantum and cryogenic behaviours of the various quantum phenomena, including eigen energies, eigen-functions, electron concentration, current characteristics, and more. This comprehensive analysis sheds light on the intricate interplay of quantum effects in nanoscale transistors under deep cryogenic conditions, offering valuable insights into the development of cryo-CMOS circuits for quantum computing.

Continuum strain of point defects

We propose a new Regularized Green's Function Method (RGFM) derived from electron densities and captures the disturbance due to point defects, successfully extending the elastic strain determination to the lattice scales. The RGFM circumvents the use of concentrated point forces, which results in unrealistic singular fields. The objective is to determine the force variations at the atomic scales from Ab-initio calculations as Quantum Mechanical Force Density (QMFD). QMFD encodes the information regarding the electronic structure of the defect since it is related to the gradients of electron wavefunctions generated from the Density Functional Theory (DFT) calculations. Once the QMFD is calculated, RGFM solves the force equilibrium equation via Fourier transforms to compute elastic fields. Therefore, the present treatment reflects the electronic structure of the atomic positions, hence the complex elastic deformations and interactions at short range, which represents a significant advancement compared to previous studies. The RGFM can also capture the long-range fields since it calculates the decay of the force fields away from the nuclei. Previous theories, such as the elastic dipole method, face two main shortcomings: they can only handle the long-range elastic fields, and contain an unphysical singularity at the center of the point defect. Our novel derivation of distributed forces addresses both challenges, i.e., it renders non-singular displacement and strain fields at the nuclei, and can also describe the elastic response accurately far from the nuclei center. The application of the method to the NV (nitrogen-vacancy) center in SiC is demonstrated in comparison with the elastic dipole theory, showing the advantages of the present methodology.

Applications of the landscape function for Schrödinger operators with singular potentials and irregular magnetic fields

We resolve both a conjecture and a problem of Z. Shen from the 90's regarding non-asymptotic bounds on the eigenvalue counting function of the magnetic Schrödinger operator La,V=−(∇−ia)2+V with a singular or irregular magnetic field B on Rn, n≥3. We do this by constructing a new landscape function for La,V, and proving its corresponding uncertainty principle, under certain directionality assumptions on B, but with no assumption on ∇B. These results arise as applications of our study of the Filoche-Mayboroda landscape function u, a solution to the equation LVu=−divA∇u+Vu=1, on unbounded Lipschitz domains in Rn, n≥1, and 0≤V∈Lloc1, under a mild decay condition on the Green's function. For LV, we prove a priori exponential decay of Green's function, eigenfunctions, and Lax-Milgram solutions in an Agmon distance with weight 1/u, which may degenerate. Similar a priori results hold for La,V. Furthermore, when n≥3 and V satisfies a scale-invariant Kato condition and a weak doubling property, we show that 1/u is pointwise equivalent to the Fefferman-Phong-Shen maximal function m(⋅,V) (also known as Shen's critical radius function); in particular this gives a setting where the Agmon distance with weight 1/u is not too degenerate. Finally, we extend results from the literature for La,V regarding exponential decay of the fundamental solution and eigenfunctions, to the situation of irregular magnetic fields with directionality assumptions.

Denoising and Extension of Response Functions in the Time Domain.

Response functions of quantum systems, such as electron Green's functions, magnetic, or charge susceptibilities, describe the response of a system to an external perturbation. They are the central objects of interest in field theories and quantum computing and measured directly in experiment. Response functions are intrinsically causal. In equilibrium and steady-state systems, they correspond to a positive spectral function in the frequency domain. Since response functions define an inner product on a Hilbert space and thereby induce a positive definite function, the properties of this function can be used to reduce noise in measured data and, in equilibrium and steady state, to construct positive definite extensions for data known on finite time intervals, which are then guaranteed to correspond to positive spectra.