C T symmetry in nonlinear time-dependent electronic structure theories.

The lattice statics Green's function method for calculation of the atomistic structure of grain boundary interfaces in solids as described in Part I is extended to include anharmonic effects. It is shown that the ‘anharmonic’ response of a solid to ‘anharmonic’ forces can be represented in terms of the ‘harmonic’ response of the solid to an effective anharmonic force. The Green's function method then requires solving a finite order nonlinear matrix equation, which is done by using standard numerical methods. For the purpose of illustration, the method is applied to calculate the atomistic structure of a ∑5 tilt boundary in fec copper.

Methods which use time-dependent orbitals for the description of quantum dynamics of electrons, like (multiconfiguration) time-dependent Hartree-Fock or time-dependent density-functional theory, produce an effectively time-dependent electronic structure. This effect is strongest if only a single determinant represents the system. Focusing on this case, we show how features of the time-dependent electronic structure show up in optimized laser pulses used for the coherent control task of a population inversion.

The enriched modified local green's function method applied to elasto static problems

A lattice statics Green's function method is described for calculating the atomistic structure of a solid near a grain boundary interface. First, a reference state is defined which is ‘near’ the equilibrium state. The Green's function for the reference state is obtained in terms of the perfect lattice Green's function by mapping the lattice sites of the reference state to the perfect lattice sites and solving the Dyson's equation within a supercell. This Green's function gives the response of the reference state which determines the atomic relaxations under the net forces which would be present in the reference state. The specific case of a ∑5 tilt boundary in a fec lattice has been considered, assuming the validity of the harmonic approximation.

Background: The time-dependent Hartree-Fock (TDHF) theory has been successful in describing low-energy heavy ion collisions. Recently, we have shown that multinucleon transfer processes can be reasonably described in the TDHF theory combined with the particle-number projection technique. Purpose: In this work, we propose a theoretical framework to analyze properties of reaction products in TDHF calculations. Methods: TDHF calculation in three-dimensional Cartesian grid representation combined with particle number projection method. Results: We develop a theoretical framework to calculate expectation values of operators in the TDHF wave function after collision with the particle-number projection. To show how our method works in practice, the method is applied to $^{24}$O+$^{16}$O collisions for two quantities, angular momentum and excitation energy. The analyses revealed following features of the reaction: The nucleon removal proceeds gently, leaving small values of angular momentum and excitation energy in nucleon removed nuclei. Contrarily, nuclei receiving nucleons show expectation values of angular momentum and excitation energy which increase as the incident energy increases. Conclusions: We have developed a formalism to analyze properties of fragment nuclei in the TDHF theory combined with the particle-number projection technique. The method will be useful for microscopic investigations of reaction mechanisms in low-energy heavy ion collisions as well as for evaluating effects of particle evaporation on multinucleon transfer cross sections.

The green's function method in quantum statistics

The green's function method for the monoenergetic transport equation with forward/backward/isotropic scattering

The time-dependent Hartree-Fock (TDHF) theory is generalized in order to include the effect of two-body collisions (i.e. the residual interaction). This is achieved by adding a collision integral into the TDHF equations, similar to the one ordinarily used in the Boltzmann equation. It is shown, that two-body collisions arise from the imaginary part of the effective interaction between two nucleons whereas the Hartree-Fock field is associated to the real part of the same interaction. There is thus no double counting when the collisions are added to a single particle field. Various approximations for the collision integral are discussed and their accuracy evaluated. Special effort is made in order to obtain conserving approximations. It is shown that for discrete fields, energy as well as momentum conservation is achieved by off-shell scattering processes. In the light of a previous paper, it is argued that two-body collisions should dominate the irreversible processes above some critical energy (roughly 200 MeV per nucleon). Below this energy the irreversible effects due to the single particle field and the collisions are expected to be of the same order of magnitude.

The family of Green's function methods based on the GW approximation has gained popularity in the electronic structure theory thanks to its accuracy in weakly correlated systems combined with its cost-effectiveness. Despite this, self-consistent versions still pose challenges in terms of convergence. A recent study [Monino and Loos J. Chem. Phys. 2022, 156, 231101.] has linked these convergence issues to the intruder-state problem. In this work, a perturbative analysis of the similarity renormalization group (SRG) approach is performed on Green's function methods. The SRG formalism enables us to derive, from first-principles, the expression of a naturally static and Hermitian form of the self-energy that can be employed in quasiparticle self-consistent GW (qsGW) calculations. The resulting SRG-based regularized self-energy significantly accelerates the convergence of qsGW calculations, slightly improves the overall accuracy, and is straightforward to implement in existing code.

Three-dimensional deformations of a curved circular beam subjected to thermo-mechanical loading using green's function method

This chapter contains sections titled: Parasitic Resistances: General Considerations Parasitic Capacitances: General Considerations Parasitic Inductances: General Considerations Approximate Formulas for Capacitances Green's Function Method: Using Method of Images Green's Function Method: Fourier Integral Approach Network Analog Method Simplified Formulas for Interconnection Capacitances and Inductances on Silicon and GaAs Substrates Inductance Extraction Using FastHenry Copper Interconnections: Resistance Modeling Electrode Capacitances in GaAs MESFET: Application of Program IPCSGV Exercises References

Electronic structure of the ideal silicon vacancy by the muffin-tin green's function method

Critical analysis of equations-of-motion—Green's function method: Ionization potentials of N2

The structure of the valence bands in KC1 is calculated by the Green's function method. The results are compared with those of Howland by the tight-binding approximation. It is found that results obtained by the two methods are in good agreement.

We present a brief pedagogical review of theoretical Green's function methods applicable to open quantum systems out of equilibrium, in general, and single molecule junctions, in particular. We briefly describe experimental advances in molecular electronics and then discuss different theoretical approaches. We then focus on Green's function methods. Two characteristic energy scales governing the physics are many-body interactions within the junctions and molecule-contact coupling. We, therefore, discuss weak interactions and weak coupling as two limits that can be conveniently treated within, respectively, the standard nonequilibrium Green's function (NEGF) method and its many-body flavors (pseudoparticle and Hubbard NEGF). We argue that the intermediate regime, where the two energy scales are comparable, can in many cases be efficiently treated within the recently introduced superperturbation dual fermion approach. Finally, we review approaches for going beyond these analytically accessible limits, as embodied by recent developments in numerically exact methods based on Green's functions.