The eigenfunction expansion of the infinite depth free surface Green function in three dimensions

ABSTRACTA new method is proposed for a fast evaluation of high-dimensional integrals of potential energy surfaces (PES) that arise in many areas of quantum dynamics. It decomposes a PES into a canonical low-rank tensor format, reducing its integral into a relatively short sum of products of low-dimensional integrals. The decomposition is achieved by the alternating least squares (ALS) algorithm, requiring only a small number of single-point energy evaluations. Therefore, it eradicates a force-constant evaluation as the hotspot of many quantum dynamics simulations and also possibly lifts the curse of dimensionality. This general method is applied to the anharmonic vibrational zero-point and transition energy calculations of molecules using the second-order diagrammatic vibrational many-body Green's function (XVH2) theory with a harmonic-approximation reference. In this application, high dimensional PES and Green's functions are both subjected to a low-rank decomposition. Evaluating the molecular integrals over a low-rank PES and Green's functions as sums of low-dimensional integrals using the Gauss–Hermite quadrature, this canonical-tensor-decomposition-based XVH2 (CT-XVH2) achieves an accuracy of 0.1 cm−1 or higher and nearly an order of magnitude speedup as compared with the original algorithm using force constants for water and formaldehyde.

We combine the recently developed many-body Green's function theory for electrons and nuclei with the exact factorization of the wave function. The existing Born-Oppenheimer Green's functions are shown to be special cases of our exact approach. We consider the limitations of the laboratory frame formulation of the Green's function theory and discuss why the body-fixed frame formulation is needed in order to go beyond the Born-Oppenheimer theory. We give exact forms of the electronic and nuclear Green's functions written in terms of the exact factorized states, providing a systematic approach beyond the Born-Oppenheimer approximation. The lowest order approximation to the exact electronic Green's function is found to be an expected value of the Born-Oppenheimer electronic Green's function with respect to the nuclear density.

Green function and density functional theories are used to study electron transport characteristics through single molecules addressed by two metallic contacts. Each contact is modeled with one nan...

ABSTRACTThe Green's function theory and high-temperature series expansions technical have been developed for magnetic systems GeNi2−xCoxO4. We have applied the Green's function theory to evaluate thermal magnetization and magnetic susceptibility for different values of magnetic field and dilution x, considering all components of the magnetization when an external magnetic field is applied in (x,z)-plane. The second theory combined with the Padé approximants method for a randomly diluted Heisenberg magnet is used to deduce the magnetic phase diagram of GeNi2 − xCoxO4 systems. The critical exponents and associated with the magnetic susceptibility and the correlation length ξ, respectively, have been deduced. The theoretical results are compared with those given by magnetic measurements.

In using the spectral theorem of many-body Green's function theory in order to relate correlations to commutator Green's functions, it is necessary in the standard procedure to consider the anti-commutator Green's functions as well whenever the matrix governing the equations of motion for the commutator Green's functions has zero eigenvalues. We show that a singular-value decomposition of this matrix allows one to reformulate the problem in terms of a smaller set of Green's functions with an associated matrix having no zero eigenvalues, thus eliminating the need for the anti-commutator functions. The procedure is quite general and easy to apply. It is illustrated for the field-induced reorientation of the magnetization of a ferromagnetic Heisenberg monolayer and it is expected to work for more complicated cases as well.

Using semiclassical approximations and graph-theoretical concepts, a path representation of the energy-dependent Green function in a one-dimensional multiple-well potential is derived. Applying uniform semiclassical methods, this representation is valid for energies close to the barrier maxima, where tunnelling and above-barrier reflection are of importance. Semiclassical quantization is discussed and a closed path representation of the density of states is derived. Applications to wavepacket dynamics and to the quantization of disordered systems are presented.

Nuclear structure theory has recently gone through a major renewal with the development of ab initio techniques that can be applied to a large number of atomic nuclei, well beyond the light sector that had been traditionally targeted in the past. Self-consistent Green's function theory is one among these techniques. The present work aims to give an overview of the self-consistent Green's function approach for atomic nuclei, including examples of recent applications and a discussion on the perspectives for extending the method to nuclear reactions, doubly open-shell systems and heavy nuclei.

We present a scalable single-particle framework to treat electronic correlation in molecules and materials motivated by Green's function theory. We derive a size-extensive Brillouin-Wigner perturbation theory from the single-particle Green's function by introducing the Goldstone self-energy. This new ground state correlation energy, referred to as Quasi-Particle MP2 theory (QPMP2), avoids the characteristic divergences present in both second-order Møller-Plesset perturbation theory and Coupled Cluster Singles and Doubles within the strongly correlated regime. We show that the exact ground state energy and properties of the Hubbard dimer are reproduced by QPMP2 and demonstrate the advantages of the approach for larger Hubbard models where the metal-to-insulator transition is qualitatively reproduced, contrasting with the complete failure of traditional methods. We apply this formalism to characteristic strongly correlated molecular systems and show that QPMP2 provides an efficient, size-consistent regularization of MP2.

Excitonic contributions to absorption and photocurrent generation in semiconductor nanostructures are described theoretically and simulated numerically using steady-state non-equilibrium Green's function theory. In a first approach, the coherent interband polarization including Coulomb corrections is determined from a Bethe-Salpeter-type equation for the equal time interband single-particle charge carrier Green's function. The effects of excitonic absorption on photocurrent generation are considered on the same level of approximation via the derivation of the corresponding corrections to the electron-photon self-energy.

The analytical forms of free-electron susceptibilities ${\ensuremath{\chi}}_{d}(q)$ and their range functions ${\ensuremath{\chi}}_{d}(r)$ are derived at nonzero temperature starting from the Green's function representation by properly evaluating the contributions from the poles of free-electron temperature Green's function for each dimension $d=1,$ 2, and 3. The present formalism produces not only ${\ensuremath{\chi}}_{d}(q)$ and ${\ensuremath{\chi}}_{d}(r)$ which show more accurate temperature-dependent behavior than our previous results for $d=1$ and 3, but also temperature-dependent two-dimensional ${\ensuremath{\chi}}_{2}(q)$ and ${\ensuremath{\chi}}_{2}(r)$ for a wide range of temperature. Our analytical results show that irrespective of dimension, the singular behavior of ${\ensuremath{\chi}}_{d}(q)$ at $q=\ifmmode\pm\else\textpm\fi{}{2k}_{F}$ becomes suppressed at nonzero temperature as the singular points transit to complex wave vectors ${2k}_{0}^{\ifmmode\pm\else\textpm\fi{}},$ and this transition causes ${\ensuremath{\chi}}_{d}(r)$ to be exponentially damped with common damping factor ${e}^{\ensuremath{-}2{\ensuremath{\eta}}_{0}\mathrm{sin}{\ensuremath{\varphi}}_{r}{k}_{F}r}\ensuremath{\sim}{e}^{\ensuremath{-}\ensuremath{\pi}{T}^{\ensuremath{'}}{k}_{F}r}$ for low enough temperature, where the exponent of the damping factor corresponds to an imaginary part of wave vectors ${2k}_{0}^{\ifmmode\pm\else\textpm\fi{}}.$ We also show that the causality relation of the response function is essential in understanding the correct behavior of ${\ensuremath{\chi}}_{d}(q)$ and ${\ensuremath{\chi}}_{d}(r)$ for all dimensions.

The direct problem for time-dependent energy transport in a two dimensional stratified planar slab is considered. An obliquely incident planar field penetrates the slab at one boundary, and the internal energy intensity distribution is determined. The intensity is represented by the Green's function, so that the problem may be solved in terms of a canonical solution. The representation is simple, and leads to a straightforward numerical algorithm. This paper is the first step in the development of a more comprehensive theory of time-dependent transport via the Green's function representation.

Tight gas reservoirs with matrix permeabilities in the microdarcy range sometimes contain zones of natural fractures with relatively high permeabilities. The development of these reservoirs requires great care in that it is essential to connect the wells with the natural fracture system in order to ensure economic well productivities. To assess the feasibility of developing such reservoirs, a study was undertaken to investigate the relative attractiveness of connecting a well to a vertical zone of high permeability either by a horizontal hole or by a massive hydraulic fracture (MHF). The first phase of the work assumed single-phase compressible flow and utilised Green's function theory to derive the transient pressure response in such complex situations. The results indicate that a horizontal hole draining a natural fracture zone compares well with connecting the well to the naturally fractured zone by a MHF, particularly in the case of short MHFs. The calculations also resulted in new principles for the interpretation of well tests for the two situations described above. For example, interpretation of the formation linear flow period when there are multiple fractures indicates fracture areas that are larger than the area of the MHF. The second phase involved numerical simulation, with mobile water both in the matrix and in the fracture systems taken into account. The results, which agree qualitatively with those of analytical methods, indicate under which conditions coning or cusping of water from the fractures into the well perforations might be expected.

We explore the impact of point defects, including oxygen vacancies (Ov), cerium interstitials (Ce-int), and hydroxyl groups (Hy), on the electronic and optical properties of bulk CeO2 using many-body Green's function theory (GW method and Bethe-Salpeter equation). Although these three defects all produce occupied electronic levels near the conduction band minimum, they impose quite different effects. Ov and Ce-intinduce strong peaks in the low-energy region of the imaginary part of the microscopic dielectric function, indicating stronger electronic screening compared to the pristine CeO2. This causes pronounced narrowing of the bandgap, e.g., by 0.8eV in G0W0 and 1.6eV in the eigenvalue self-consistent GW for Ov. Comparatively, Hy affects little electronic screening and bandgap at different levels of GW calculations. For the lowest several 4f orbitals, the exchange part of the self-energy (|Σx| > 9eV) in GW is much stronger than the correlation part (|Σc| < 5eV) for Ov and Ce-int, while |Σc| is much stronger than |Σx| instead for the pristine CeO2 and Hy. Quasiparticle weights in Ov and Ce-intdecrease by a large quantity compared to the pristine CeO2. Consideration of Ov and Ce-intmight to some extent relieve the discrepancy between the GW bandgap of the pristine CeO2 and the experimental gap. Ov and Ce-intcould reduce the excitonic binding energy several times and result in optical absorption, which corresponds to the experiments.

New silicon hydrogen infrared vibrational band associated to HSiCl configurations in an amorphous silicon matrix : Green's function theory approach

The purpose of this research is to derive the spectral representation of Green's function for an acoustic layered medium by means of the concept of the Hyperfunction. The concept of the Hyperfunction used here is that the Hyperfunction is the result of the difference of the boundary values of the wave function on the spectrum in the complex wavenumber plane. The eigenfunction for the continuous spectrum is assumed to be the Hyperfunction due to Green's functi oni n the resolvent set. Green's function in the resolvent set satisfies the radiation condition, so that the definition and calculation for the energy integral for the continuous spectrum is carried out without any difficulty. As a result, the kernel of the integral for the continuous spectrum is decomposed into eigenfunctions. The decompoesd form agrees with the previous result which the author showed.