Green Function Research Articles

Laplacian operator and its square lattice discretization: Green function vs. Lattice Green function for the flat 2-torus and other related 2D manifolds

Abstract The paper investigates the truncation error between the Green function and the lattice Green function (LGF) for the Laplacian operator defined on the 2-torus and its discretization on a regular square lattice. Extensions to the cylinder and the rectangular domain with free (or Neumann) boundary conditions are also proposed. In each of these instances, the Green function and its discrete analog are given in exact analytical closed-form allowing to infer accurate estimates as the lattice spacing tends to zero. As expected, it is shown that the continuum limit of the LGF coincides well with the Green function in every case. In particular, the issue of logarithmic singularity regularization of the Green function by the lattice discretization is addressed through two related application examples regarding the rectangular domain, and devoted to the computation of corner-to-corner resistance of an electrical conducting square and the mean first-passage time between the diagonally opposite vertices of a square for a standard Brownian motion, both derived considering the continuum limit.

Nodal spectral functions stabilized by non-Hermitian topology of quasiparticles

In quantum materials, basic observables such as spectral functions and susceptibilities are determined by Green's functions and their complex quasiparticle spectrum rather than by bare electrons. Even in closed many-body systems, this makes a description in terms of effective non-Hermitian (NH) Bloch Hamiltonians natural and intuitive. Here, we discuss how the abundance and stability of nodal phases is drastically affected by NH topology. While previous work has mostly considered complex degeneracies known as exceptional points as the NH counterpart of nodal points, we propose to relax this assumption by only requiring a crossing of the real part of the complex quasiparticle spectra, which entails a band crossing in the spectral function, i.e., a nodal spectral function. Interestingly, such real crossings are topologically protected by the braiding properties of the complex Bloch bands, and thus generically occur already in one-dimensional systems without symmetry or fine tuning. We propose and study a microscopic lattice model in which a sublattice-dependent interaction stabilizes nodal spectral functions. Besides the gapless spectrum, we identify nonreciprocal charge transport properties after a local potential quench as a key signature of nontrivial band braiding. Finally, in the limit of zero interaction on one of the sublattices, we find a perfectly ballistic unidirectional mode in a nonintegrable environment, reminiscent of a chiral edge state known from quantum Hall phases. Our analysis is corroborated by numerical simulations both in the framework of exact diagonalization and within the conserving second Born approximation. Published by the American Physical Society 2024

Sustainability and Capability Building in Organizations: A Focused Group Approach

This study investigates business sustainability and the development of comprehensive capabilities that are crucial for future-ready organizations. It delineates the sustainable business practices that are necessary to enhance the functional, operational, technological and strategic dimensions of an organization. Furthermore, we examine methods to augment a firm’s capacity to foster sustainable growth. The authors utilized a structured approach; four focused group discussions (FGDs) were conducted with experts from multinational firms to garner real-time industry insights in the context of the new normal. The discussions emphasized key practices such as change management, competency building, green business functions, regenerative strategies, empathetic leadership and the triple bottom line approach. This research underscores the real-time business practices implemented during and after the pandemic to address and mitigate the disruptions caused by the outbreak.

GW with hybrid functionals for large molecular systems

A low-cost approach for stochastically sampling static exchange during time-dependent Hartree–Fock-type propagation is presented. This enables the use of an excellent hybrid density functional theory (DFT) starting point for stochastic GW quasiparticle energy calculations. Generalized Kohn–Sham molecular orbitals and energies, rather than those of a local-DFT calculation, are used for building the Green function and effective Coulomb interaction. The use of an optimally tuned hybrid diminishes the starting point dependency in one-shot stochastic GW, effectively avoiding the need for self-consistent GW iterations.

Spin-2 Green’s functions on Kerr in radiation gauge

Abstract We construct retarded and advanced Green's functions for gravitational perturbations in Kerr in an ingoing radiation gauge. Our Green's functions have a frequency domain piece that has previously been obtained by Ori [Phys. Rev. D 67 (2003)] based on the Chrzanowski-Cohen-Kegeles metric reconstruction method. As is well known, this piece by itself is not sufficient to obtain an actual Green's function. We show how to complete it with a piece based on a method by Green et al. [Class. Quant. Grav. 37 (2020)]. The completion piece has a completely explicit form in the time-domain and is supported on pairs of points on the same outgoing principal null geodesic which are in the appropriate causal order. We expect our Green's functions to be useful for gravitational self-force calculations and other perturbation problems on Kerr spacetime.

Solvability of a sixth‐order boundary value problem with multi‐point and multi‐term integral boundary conditions

This paper aims to investigate the existence and uniqueness of solutions for a sixth‐order differential equation involving nonlocal and integral boundary conditions. Firstly, we obtain the properties of the relevant Green's functions. The existence result of at least one nontrivial solution is obtained by applying the Krasnoselskii–Zabreiko fixed point theorem. Moreover, we also establish the existence of unique solution to the considered problem via Hölder and Minkowski inequalities and Rus's theorem. Finally, two numerical examples are included to show the applicability of our main results.

Enhanced framework for solving general energy equations based on metropolis-hasting Markov chain Monte Carlo

Due to the widespread presence of heat and mass transfer phenomena in industrial applications, numerous studies have been devoted to the accurate solution of energy equations, providing a foundation for the analysis of heat and mass transfer processes in practical applications. In this study, a Green's Function Markov Superposition Monte Carlo (GMSMC) for solving general energy equations has been developed based on probability and statistical principles owing to its advantageous features of insensitivity towards dimension and geometric complexity as well as the capability to handle multiple integrals in complex domains. The energy equation is first decomposed, and corresponding probability models are established for each component, considering their interrelationships. Subsequently, a solution framework for solving the general energy equation is constructed by integrating these probability models based on a Markov chain structure. The mathematical principles and formulae of the proposed method are derived in detail. The performance of the proposed method is validated by several heat transfer systems with different combinations of boundary conditions and features, which mainly include the distribution of the internal heat source and whether the convection or transient term is included. Results of the validation show that the temperatures obtained by the proposed method are in good agreement with the FEM based on a fine grid, no matter whether the calculation is for a single point or a distribution.

Strong dipole-dipole interactions via enhanced light-matter coupling in composite nanofiber waveguides

We study the interaction of emitters with a composite waveguide formed from two parallel optical nanofibers in regimes of experimental importance for atomic gases or solid-state emitters. Using the exact dyadic Green's function we comprehensively investigate the coupling efficiency and the fiber-induced Lamb shift accounting for variations in emitter positions and fiber configurations. This reveals coupling efficiencies and Purcell factors that are enhanced considerably beyond those using a single fiber waveguide, and robustness in the figures of merit. We finally investigate resonant dipole-dipole interactions and the generation of entanglement between two emitters mediated through the composite waveguide under excitation. We show that the concurrence can be enhanced for two fiber systems, such that entanglement may be present even in cases where it is zero for a single fiber. All-fiber systems are simple in construction and benefit from a wealth of existing telecommunications technologies, while enjoying strong couplings to emitters and offering interesting light-matter functionalities specific to slot waveguides. Published by the American Physical Society 2024

On Zero-Temperature Current through Atomic Chain Subjected to a Uniformly Varying Field: Green's Function Formalism

On the basis of the tight-binding formalism and Green’s function technique, we obtain all matrix elements of Green’s functions for a biased chain with linear variations of the electron on-site energy. Their dependence on system parameters is analyzed in the context of through-molecule electron transport.

Efficient Algorithm for Extracting Transmission Spectrum From Band Structure in Low‐Dimensional Systems

AbstractAiming at an efficient method to determine the transport properties of a physical system, an effective and accurate band‐counting algorithm is presented to extract the transmission spectrum of a low‐dimensional system, directly from the band structure. This approach is more efficient than Hamiltonian‐dependent formalisms such as the standard Green's function (GF) or the transfer matrix methods. The only constraint of the approach is that the bands should not be mixed, i.e., for each band in the k‐path, there should be a set of eigenvalues. The efficiency of the approach is comparable to that of Green's function method, and it is applicable to any computational approach whose output is a band structure, whether for particles or quasiparticles such as electrons and phonons. Since the transport coefficient is calculated separately for each band, the occurrence of eigenvalues at the same k‐point can be captured by the algorithm. The proposed algorithm will be useful for studying transmission coefficient‐dependent quantities, such as thermoelectric‐related quantities, and also the electric current within the Landauer–Büttiker formalism.

Exact scattering cross section for lattice-defect scattering of phonons using the atomistic Green's function method

Exact scattering cross section for lattice-defect scattering of phonons using the atomistic Green's function method

Thermal Transport at the AlN-SiC Interface and Grain Boundary of AlN.

AlN is deposited on silicon carbide (SiC) for high-power electronics; in these devices, AlN acts as both a buffer layer for the growth of the active device and a thermal conductor. However, the mechanism of thermal transport through the AlN-SiC interfaces and through grain boundaries of AlN has not been clearly analyzed, even though AlN forms grain boundaries during the deposition process. The thermal properties of the AlN-SiC interface and the inversion domain boundaries (IDBs) of AlN were examined by a phonon transport model based on a nonequilibrium Green function formalism and first-principles calculations. The interface and grain boundary models were designed, and the thermal resistances (TRs) and origins of TR were examined. The TRs of the AlN-SiC interface and the IDB of AlN are much higher than the TRs of AlN and SiC of relevant thickness. Elemental intermixing and vacancy formation were modeled. The formation of charge-balanced defect of VAl + 3ON is thermodynamically favorable compared to other defects, indicating that ON induces formation of VAl. The charge-balanced defect combining VAl and ON increases the TRs of both AlN-SiC interfaces and AlN grain boundaries because vacancy defects induce larger changes in mass than all other defects, and TRs are proportional to changes in mass. In addition, VAl defects are increased by excess ON, resulting in a continuous increase in TR, and then, the calculated thermal boundary resistance (TBR) of the AlN-SiC interface with increased density of VAl by excess ON reaches the experimental TBR. Therefore, it is expected that the large increase in TR by the formation of VAl + ON would be suppressed by controlling the low O density during synthesis.

Study of Dependence of the Energy of the Field in Weakly Conductive Fiberlight-Guide with Gradient Refractive Index Profile Without Regard to Polarization

A round-in-cross-section weakly guiding fiber optic light guide is considered. The system of Maxwellian equations for electrically conductive transparent media without due regard to polarization with an index of refraction in the case under consideration is reduced to the homogeneous Helmholtz equation, a particular solution of which is found using the Green's function. For a unimodalmode a common decision was obtained for the field and energy inside the fiber in the general case of a gradient refractive index profile depending on the radial coordinate. The concept of normalized energy is introduced as the ratio of the energy inside a fiber with gradient refractive index profile to the energy inside a fiber with a step-index profile. Since in a single-mode regime the zero-order Bessel function, which describes the field inside a step-index profile fiber, can be replaced by a Gaussoid, then, when extending this replacement to the case of a single-mode gradient fiber, as a first approximation we shall obtain a finite expression for the normalized energy for a general gradient profile. The dependences of the normalized energy on the waveguide number were obtained for each of the degrees from the first to the fourth inclusive. It is shown that in the considered approximation, the energy increases up to a certain parameter values (for the first degree – a triangle profile) or slowly decreases (other profiles), after this value the energy increases for all profiles. The results obtained will help to select a suitable single-mode fiber for practical application.

Extracting fault-zone structures using the virtual seismometer method: from theoretical to synthetic test

Summary Rocks near a fault plane are commonly damaged by multiple earthquake ruptures, forming damage zones. The damage zone is important structures controlling various properties of a fault, yet its fine scale (tens to hundreds of meters) structure is difficult to resolve with surface seismic observations. We propose to use earthquakes that occur at depth within a fault zone as virtual seismometers (VSs) and use surface observations to extract Green's function (GFs) between VS pairs (VSGFs) . This method resembles that of ambient noise tomography and the retrieved VSGFs are related to the structures between event pairs. In this study, we develop the theory about how to extract VSGFs using surface stations deployed across a fault zone. Firstly, we use a half-space model and Fresnel zone analysis to determine the upper and lower limits of the GF frequency band, which is controlled by the station spacing and aperture of a given seismic array. Then, for VS in a fault zone, we demonstrate that the VSGF can be retrieved by linear seismic arrays deployed across the fault, and that the VSGF is equivalent to waves emitted simultaneously from an array of mirror sources of one event and received by the other. Secondly, the half-space result is directly adopted to determine the corresponding frequency band in the damage zone situation. Thirdly, we analyze different combinations of VS pair geometry and conclude that a relatively larger VS distance (much larger than the damage zone width) is more effective to recover damage zone structures for the available frequency bands. In this situation, VSGFs are trapped waves, that is represented by the interference of mirror sources. In such a case, the trapped waves are equivalent to surface waves, which have dispersion features to extract damage zone structures. Finally, we adopt the VSGF method to the Ridgecrest earthquake aftershock monitoring array and use a profile of aftershocks to extract 6 pairs of VSGFs. The spatial variation of VSGFs may reflect the depth-dependent variation of damaged zone. Our analysis shows a promising direction to use VSGFs to extract spatial variations of fault damaged zones.

Enhancement of tunneling electroresistance in metal/two-dimensional ferroelectric tunnel junctions: Route for polarization-modulated interface transport.

In fabricating ferroelectric tunnel junction (FTJ) devices, it is essential to employ low-resistance metals as electrodes interfacing with two-dimensional (2D) ferroelectric materials. For FTJs with a top contact configuration, two interfaces for charge transport are present, namely the vertical interface between the metal electrode and the 2D ferroelectric material, and the lateral interface between the
electrode and the central scattering region. These interfaces significantly influence the tunneling electroresistance (TER) of FTJs. However, there exists a notable deficiency
in comprehension concerning the physics of charge transport at the interface. In this
work, we explore the interface transport properties in FTJs featuring a top contact configuration between metal and the typical α-In2Se3 monolayer. By employing the non-equilibrium Green's function method, we observe a TER ratio of 1.15 × 105% for
the Pd top contact interfacing with an α-In2Se3 monolayer. The significant TER effect is attributed to polarization-controlled interface transport, which is further
elucidated through an analysis of the transport mechanisms influenced by the out of-plane polarization of α-In2Se3 at the vertical interface and the in-plane polarization at the lateral interface. This investigation of the fundamental physical mechanisms
of polarization-controlled interface transport demonstrates significant potential for enhancing non-volatile memory devices.

Coherent photo- and electroproduction of charmonia on nuclear targets revisited: Green function formalism

Coherent photo- and electroproduction of charmonia on nuclear targets revisited: Green function formalism

Enhancing TFET performance through gate length optimization and doping control in phosphorene nanoribbons

In this study, the performance of armchair phosphorene nanoribbons (APNRs) tunnel field-effect transistors (TFETs) is compared to that of conventional Metal-Oxide-Semiconductor Field-Effect Transistors (MOSFETs) based on the self-consistent solution of the Poisson and Schrödinger equation within the non-equilibrium Green's Function formalism and a tight-binding Hamiltonian. As channel length decreases, undesirable consequences such as increased OFF-current and sub-threshold swing can affect MOSFETs' performance. The study thoroughly investigates various aspects of TFET performance, including the impact of channel length, gate length, and doping on parameters like ON-current, OFF-current, the ON-/OFF-current ratio, and sub-threshold swing. An important finding of this research relates to the influence of source and drain doping. We demonstrate that fine-tuning impurity levels directly affects phosphorene nanoribbon TFET (PTFET) performance. The article also investigates the impact of gate length on PTFET performance. New transistor configurations with different gate lengths are proposed in this research. The study shows that optimizing gate length can significantly reduce OFF-current. Furthermore, the combined impact of gate length and doping concentration on PTFET performance is investigated. Through the strategic extension of the gate length towards the drain side and precise adjustments in doping levels, notable improvements in subthreshold swings, ON-current, and the ON-/OFF-current ratio can be realized.

Susceptible Detection of Organic Molecules Based on C3B/Graphene and C3N/Graphene van der Waals Heterojunction Gas Sensors.

Constructing van der Waals (vdW) heterostructures is a prospective approach that is essential for developing a new generation of functional two-dimensional (2D) materials and designing new conceptual nanodevices. Using density-functional theory combined with a nonequilibrium Green's function approach allows for the theoretical and systematic exploration of the electronic structure, transport properties, and sensitivity of organic small molecules adsorbed on 2D C3B/graphene (Gra) and C3N/Gra vdW heterojunctions. Calculations show the metallic properties of C3B/Gra and C3N/Gra after the formation of heterojunctions. Interestingly, the heterojunctions C3B/Gra (C3N/Gra) for the adsorption of small organic molecules (C2H2, C2H4, CH3OH, CH4, and HCHO) at the C3B (C3N) side are sensitive to the chemisorption of C2H2 and C2H4. Similarly, the Gra/C3B is chemisorbed for both C2H2 and C2H4 when adsorbed on Gra side, while it is only chemisorbed for C2H2 in Gra/C3N. Interestingly, all heterojunctions on different sides are physisorbed for CH3OH, CH4, and HCHO. Furthermore, the calculated I-V curves demonstrate that the devices based on the adsorption of C2H2 and C2H4 at each side of the heterojunction have remarkable anisotropy, in with the current being considerably greater in the zigzag direction than in the armchair direction. More specifically, with C2H2 adsorbed on the Gra side, the sensitivity along the armchair direction is up to 85.0% for Gra/C3B and close to 100% for Gra/C3N. This study reveals that C3B/Gra (C3N/Gra) heterojunctions with high selectivity, high anisotropy, and excellent sensitivity are highly prospective 2D materials for applications, which further contributes new insights into the development of future electronic nanodevices.

Holography Optimization based on combining Iterative Green's Function algorithm and Deep Learning Method

Holography Optimization based on combining Iterative Green's Function algorithm and Deep Learning Method

Active control of noise radiated from a long cylinder: Can the Nyquist limitation be broken?

In the present paper, we consider active control of noise propagating from a long cylinder. For that purpose control sources are distributed on the external surface of the cylinder. They provide a secondary sound field which enables them to compensate for the noise field propagating outside. To implement active noise control, we apply an approach based on the Calderón potentials that have the projection property. Numerical simulations to attenuate broadband noise with different numbers of control sources per wavelength are carried out. The effect of the cylinder on the Green's function and consequent noise attenuation is studied. There are two key findings in this paper. First, the results demonstrate that the level of relative noise attenuation remarkably increases along with the growth of the distance. Second, it is shown that even less than two control sources per wavelength can provide essential noise cancelation. At first glance, this result contradicts the well-known Nyquist-Shannon sampling theorem. A theoretical explanation of this result is provided.