Green function theory of ferromagnetism
Green function theory of ferromagnetism used to examine implications of cube-root behavior of magnetization near Curie point
MAGNETIZATION↗
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Step-by-Step Simulation of Radiation Chemistry Using Green Functions for Diffusion-Influenced Reactions
Radiolytic species are formed approximately 1 ps after the passage of ionizing radiation through matter. After their formation, they diffuse and chemically react with other radiolytic species and neighboring biological molecules, leading to various oxidative damage. Therefore, the simulation of radiation chemistry is of considerable importance to understand how radiolytic species damage biological molecules [1]. The step-by-step simulation of chemical reactions is difficult, because the radiolytic species are distributed non-homogeneously in the medium. Consequently, computational approaches based on Green functions for diffusion-influenced reactions should be used [2]. Recently, Green functions for more complex type of reactions have been published [3-4]. We have developed exact random variate generators of these Green functions [5], which will allow us to use them in radiation chemistry codes. Moreover, simulating chemistry using the Green functions is which is computationally very demanding, because the probabilities of reactions between each pair of particles should be evaluated at each timestep [2]. This kind of problem is well adapted for General Purpose Graphic Processing Units (GPGPU), which can handle a large number of similar calculations simultaneously. These new developments will allow us to include more complex reactions in chemistry codes, and to improve the calculation time. This code should be of importance to link radiation track structure simulations and DNA damage models.
Plante, Ianik↗
Nonequilibrium diagrammatic technique for Hubbard Green functions
Here, we introduce diagrammatic technique for Hubbard nonequilibrium Green functions. The formulation is an extension of equilibrium considerations for strongly correlated lattice models to description of current carrying molecular junctions. Within the technique intra-system interactions are taken into account exactly, while molecular coupling to contacts is used as a small parameter in perturbative expansion. We demonstrate the viability of the approach with numerical simulations for a generic junction model of quantum dot coupled to two electron reservoirs.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
Positivity of the Spectral Densities of Retarded Floquet Green Functions
Periodically driven nonequilibrium many-body systems are interesting because they have quasi-energy spectra, which can be tailored by controlling the external driving fields. We derive the general spectral representation of retarded Green functions in the Floquet regime, thereby generalizing the well-known Lehmann representation from equilibrium many-body physics. Here, the derived spectral Floquet representation allows us to prove the non-negativity of spectral densities and to determine exact spectral sum rules, which can be employed to benchmark the accuracy of approximations to the exact Floquet many-body Green functions.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Real-time coupled-cluster approach for the cumulant Green's function
Green’s function methods within many-body perturbation theory provide a general framework for treating electronic correlations in excited states. Here we investigate the cumulant form of the one-electron Green’s function based on the coupled-cluster equation of motion approach in an extension of our previous study. The approach yields a non-perturbative expression for the cumulant in terms of the solution to a set of coupled first order, non-linear differential equations. The method thereby adds non-linear corrections to traditional cumulant methods linear in the self energy. The approach is applied to the core-hole Green’s function and illustrated for a number of small molecular systems. For these systems we find that the non-linear contributions lead to significant improvements both for quasiparticle properties such as core-level binding energies, as well as the satellites corresponding to inelastic losses observed in photoemission spectra.
Vila, Fernando D.↗
High frequency green function for aerodynamic noise in moving media. I - General theory. II - Noise from a spreading jet
It is shown how a high frequency analysis can be made for general problems involving flow-generated noise. In the parallel shear flow problem treated by Balsa (1976) and Goldstein (1982), the equation governing sound propagation in the moving medium could be transformed into a wave equation for a stationary medium with an inhomogeneous index of refraction. It is noted that the procedure of Avila and Keller (1963) was then used to construct a high frequency Green function. This procedure involves matching a solution valid in an inner region around the point source to an outer, ray-acoustics solution. This same procedure is used here to construct the Green function for a source in an arbitrary mean flow. In view of the fact that there is no restriction to parallel flow, the governing equations cannot be transformed into a wave equation; the analysis therefore proceeds from the equations of motion themselves.
Durbin, P. A.↗
Relativistic dynamics, Green function and pseudodifferential operators
The central role played by pseudodifferential operators in relativistic dynamics is known very well. In this work, operators like the Schrodinger one (e.g., square root) are treated from the point of view of the non-local pseudodifferential Green functions. Starting from the explicit construction of the Green (semigroup) theoretical kernel, a theorem linking the integrability conditions and their dependence on the spacetime dimensions is given. Relativistic wave equations with arbitrary spin and the causality problem are discussed with the algebraic interpretation of the radical operator and their relation with coherent and squeezed states. Also we perform by means of pure theoretical procedures (based in physical concepts and symmetry) the relativistic position operator which satisfies the conditions of integrability: it is a non-local, Lorentz invariant and does not have the same problems as the “local”position operator proposed by Newton and Wigner. Physical examples, as zitterbewegung and rogue waves, are presented and deeply analyzed in this theoretical framework.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Effective spin-mixing conductance of topological-insulator/ferromagnet and heavy-metal/ferromagnet spin-orbit-coupled interfaces: A first-principles Floquet-nonequilibrium Green function approach
The spin-mixing conductance (SMC) is a key quantity determining efficiency of spin transport across interfaces. Thus, knowledge of its precise value is required for accurate measurement of parameters quantifying numerous effects in spintronics, such as spin-orbit torque, spin Hall magnetoresistance, spin Hall effect, and spin pumping. However, the standard expression for SMC, provided by the scattering theory in terms of the reflection probability amplitudes, is inapplicable when strong spin-orbit coupling (SOC) is present directly at the interface. This is the precisely the case of topological-insulator/ferromagnet and heavy-metal/ferromagnet interfaces of great contemporary interest. We introduce an approach where first-principles Hamiltonian of these interfaces, obtained from noncollinear density functional theory (ncDFT) calculations, is combined with charge-conserving Floquet-nonequilibrium-Green-function formalism to compute directly the pumped spin current $I^{S_z}_L$ into semi-infinite left lead of two-terminal heterostructures Cu/X/Co/Cu or Y/Co/Cu—where X = Bi 2 Se 3 and Y = Pt or W—due to microwave-driven steadily precessing magnetization of the Co layer. This allows us to extract an effective SMC as a prefactor in $I^{S_z}_L$ versus precession cone angle θ dependence, as long as it remains the same, $I^{S_z}$ ∝ sin 2 θ , as in the case where SOC is absent. By comparing calculations where SOC in switched off versus switched on in ncDFT calculations, we find that SOC consistently reduces the pumped spin current and therefore the effective SMC.
36 MATERIALS SCIENCE↗
Coupled cluster Green function: Model involving single and double excitations
In this paper, we report on the development of a parallel implementation of the coupled-cluster (CC) Green function formulation (GFCC) employing single and double excitations in the cluster operator (GFCCSD). A key aspect of this work is the determination of the frequency dependent self-energy, Σ(ω). The detailed description of the underlying algorithm is provided, including approximations used that preserve the pole structure of the full GFCCSD method, thereby reducing the computational costs while maintaining an accurate character of methodology. Furthermore, for systems with strong local correlation, our formulation reveals a diagonally dominate block structure where as the non-local correlation increases, the block size increases proportionally. Here, to demonstrate the accuracy of our approach, several examples including calculations of ionization potentials for benchmark systems are presented and compared against experiment.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
Spin pumping from antiferromagnetic insulator spin-orbit-proximitized by adjacent heavy metal: a first-principles Floquet-nonequilibrium Green function study
Motivated by the recent experiment on spin pumping from sub-THz radiation-driven uniaxial antiferromagnetic insulator (AFI) MnF 2 into heavy metal (HM) Pt hosting strong spin-orbit (SO) coupling, we compute and compare pumped spin currents in Cu/MnF 2 /Cu and Pt/MnF 2 /Cu heterostructures. Recent theories of spin pumping by AFI have relied on simplistic Hamiltonians (such as tight-binding) and the scattering approach to quantum transport yielding the so-called interfacial spin mixing conductance (SMC), but the concept of SMC ceases to be applicable when SO coupling is present directly at the interface. In contrast, we use a more general first-principles quantum transport approach which combines noncollinear density functional theory with Floquet-nonequilibrium Green's functions in order to take into account: SO-proximitized AFI as a new type of quantum material, different from isolated AFI and brought about by AFI hybridization with adjacent HM layer; strong SO coupling at the interface; and evanescent wavefunctions penetrating from Pt or Cu into AFI layer to make its interfacial region conducting rather than insulating as in the isolated AFI. The DC component of pumped spin current $I_\mathrm{DC}^{S_z}$ vs. precession cone angle $\theta_{\boldsymbol{l}}$ of the Néel vector l of AFI does not follow putative $I^{S_z}_\mathrm{DC} \propto \sin^2 \theta_{\boldsymbol{l}}$, except for very small angles $\theta_{\boldsymbol{l}} \lesssim 10^\circ$ for which we define an effective SMC from the prefactor and find that it doubles from MnF2/Cu to MnF2/Pt interface. In addition, the angular dependence $I^{S_z}_\mathrm{DC}(\theta_{\boldsymbol{l}})$ differs for opposite directions of precession of the Néel vector, leading to twice as large SMC for the right-handed than for the left-handed chirality of the precession mode.
36 MATERIALS SCIENCE↗
Calibrating the ECCO ocean general circulation model using Green's functions
Green's functions provide a simple, yet effective, method to test and calibrate General-Circulation-Model(GCM) parameterizations, to study and quantify model and data errors, to correct model biases and trends, and to blend estimates from different solutions and data products.
ocean data assimilation↗
Step-by-Step Simulation of Radiation of Radiation Chemistry Using Green Functions for Diffusion-Influenced Reactions
The irradiation of biological systems leads to the formation of radiolytic species such as H(raised dot), (raised dot)OH, H2, H2O2, e(sup -)(sub aq), etc.[1]. These species react with neighboring molecules, which result in damage in biological molecules such as DNA. Radiation chemistry is there for every important to understand the radiobiological consequences of radiation[2]. In this work, we discuss an approach based on the exact Green Functions for diffusion-influenced reactions which may be used to simulate radiation chemistry and eventually extended to study more complex systems, including DNA.
Plante, Ianik↗
A Radiation Chemistry Code Based on the Greens Functions of the Diffusion Equation
Ionizing radiation produces several radiolytic species such as.OH, e-aq, and H. when interacting with biological matter. Following their creation, radiolytic species diffuse and chemically react with biological molecules such as DNA. Despite years of research, many questions on the DNA damage by ionizing radiation remains, notably on the indirect effect, i.e. the damage resulting from the reactions of the radiolytic species with DNA. To simulate DNA damage by ionizing radiation, we are developing a step-by-step radiation chemistry code that is based on the Green's functions of the diffusion equation (GFDE), which is able to follow the trajectories of all particles and their reactions with time. In the recent years, simulations based on the GFDE have been used extensively in biochemistry, notably to simulate biochemical networks in time and space and are often used as the "gold standard" to validate diffusion-reaction theories. The exact GFDE for partially diffusion-controlled reactions is difficult to use because of its complex form. Therefore, the radial Green's function, which is much simpler, is often used. Hence, much effort has been devoted to the sampling of the radial Green's functions, for which we have developed a sampling algorithm This algorithm only yields the inter-particle distance vector length after a time step; the sampling of the deviation angle of the inter-particle vector is not taken into consideration. In this work, we show that the radial distribution is predicted by the exact radial Green's function. We also use a technique developed by Clifford et al. to generate the inter-particle vector deviation angles, knowing the inter-particle vector length before and after a time step. The results are compared with those predicted by the exact GFDE and by the analytical angular functions for free diffusion. This first step in the creation of the radiation chemistry code should help the understanding of the contribution of the indirect effect in the formation of DNA damage and double-strand breaks.
Plante, Ianik↗
Performance of wave function and Green's function methods for non-equilibrium many-body dynamics
Theoretical descriptions of the non-equilibrium dynamics of quantum many-body systems essentially employ either (i) explicit treatments, relying on the truncation of the expansion of the many-body wave function, (ii) compressed representations of the many-body wave function, or (iii) evolution of an effective (downfolded) representation through Green's functions. In this work, we select representative cases of each of the methods and address how these complementary approaches capture the dynamics driven by intense field perturbations to non-equilibrium states. Under strong driving, the systems are characterized by strong entanglement of the single-particle density matrix and natural populations approaching those of a strongly interacting equilibrium system. We generate a representative set of results that are numerically exact and form a basis for a critical comparison of the distinct families of methods. We demonstrate that the compressed formulation based on similarity-transformed Hamiltonians (coupled-cluster approach) is practically exact in weak fields and, hence, weakly or moderately correlated systems. Coupled cluster, however, struggles for strong driving fields, under which the system exhibits strongly correlated behavior, as measured by the von Neumann entropy of the single-particle density matrix. The dynamics predicted by Green's functions in the (widely popular) G W approximation are less accurate, but improve significantly upon the mean-field results in the strongly driven regime. Published by the American Physical Society 2025
Reeves, Cian C. (ORCID:0009000642581845)↗
Corrigendum to “Topological invariant in terms of the Green functions for the Quantum Hall Effect in the presence of varying magnetic field” [Ann. Phys., NY 418 (2020) 168179]
We correct misprints found in the text of the paper.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Green functions of currents in the odd-intrinsic parity sector of QCD
The independent operator basis of the most important resonances in the odd-intrinsic parity sector of QCD allows us to construct Lagrangians for corresponding Feynman diagrams of several types of interaction channels of the mesons and resonances. Here, we will discuss all three-point current correlators non-trivial for this sector. We briefly summarize their basic properties and high energy behaviour via the operator product expansion (OPE) framework. We also show that the vector field formalism is not compatible with the OPE, and for this reason the antisymmetric field formalism is a more suitable choice. We also briefly introduce some fundamental phenomological aspects that could be useful in the next studies.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
An SYK-inspired model with density–density interactions: Spectral & wave function statistics, Green’s function and phase diagram
The Sachdev–Ye–Kitaev (SYK) model is a rare example of a strongly-interacting system that is analytically tractable. Tractability arises because the model is largely structureless by design and therefore artificial: while the interaction is restricted to two-body terms, interaction matrix elements are “randomized” and therefore the corresponding interaction operator does not commute with the local density. Unlike conventional density–density-type interactions, the SYK-interaction is, in this sense, not integrable. We here investigate a variant of the (complex) SYK model, which restores this integrability. It features a randomized single-body term and a density–density-type interaction. We present numerical investigations suggesting that the model exhibits two integrable phases separated by several intermediate phases including a chaotic one. The chaotic phase carries several characteristic SYK-signatures including in the spectral statistics and the frequency scaling of the Green’s function and therefore should be adiabatically connected to the non-Fermi liquid phase of the original SYK model. Thus, our model Hamiltonian provides a bridge from the SYK-model towards microscopic realism.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗