Related papers: Variational solution of the T-matrix integral equa…
The $T$-matrix formally describes the solution of any electromagnetic scattering problem by a given particle in a given medium at a given wavelength. As such it is commonly used in a number of contexts, for example to predict the…
The hopping matrix element $t$ quantifies the quantum-mechanical coupling between frontier orbitals on a pair of nearby molecules. Convenient and generally applicable methods to determine $t$ from DFT calculations are lacking; $t$ can be…
Eigenvalue transformations, which include solving time-dependent differential equations as a special case, have a wide range of applications in scientific and engineering computation. While quantum algorithms for singular value…
A field-theoretic formulation of the exponential-operator technique is applied to a Hamiltonian eigenvalue problem in electrodynamics, quantized in light-front coordinates. Specifically, we consider the dressed-electron state, without…
We analyze the role of spatial electronic correlations and, in particular, of the magnetic fluctuations in Mott insulators. A half-filled Hubbard model is solved at large strength of the repulsion U on a two-dimensional square lattice using…
Richardson approach provides an exact solution of the pairing Hamiltonian. This Hamiltonian is characterized by the electron-hole pairing symmetry, which is however hidden in Richardson equations. By analyzing this symmetry and using an…
We develop computational methods for approximating the solution of a linear multi-term matrix equation in low rank. We follow an alternating minimization framework, where the solution is represented as a product of two matrices, and…
We extend Merrifield's Variational Ansatz in the variational band theory of polarons to cover a frame of two electronic bands mixed by an Einstein phonon. The Hamiltonian is composed of the local and hopping energy terms, the vibrational…
Due to non-linear structure, iterative Green's function methods can result in multiple different solutions even for simple molecular systems. In contrast to the wave-function methods, a detailed and careful analysis of such molecular…
When a wave, such as sound or light, scatters within a densely packed particulate, it can be rescattered many times between the particles, which is called multiple scattering. Multiple scattering can be unavoidable when: trying to use sound…
The Dirac equation for H$_2^+$ is solved numerically using an iterative method proposed by Kutzelnigg [Z. Phys. 11, 15 (1989]. The four-component wavefunction is expanded in a newly introduced kinetically balanced exponential basis set. The…
The two-body t-matrix is calculated directly as function of two vector momenta for different Malfliet-Tjon type potentials. At a few hundred MeV projectile energy the total amplitude is quite a smooth function showing only a strong peak in…
A variational method is used to derive a self-consistent macro-particle model for relativistic electromagnetic kinetic plasma simulations. Extending earlier work [E. G. Evstatiev and B. A. Shadwick, J. Comput. Phys., vol. 245, pp. 376-398,…
We identify a set of Hertz potentials for solutions to the vector wave equation on black hole spacetimes. The Hertz potentials yield Lorenz gauge electromagnetic vector potentials that represent physical solutions to the Maxwell equations,…
The grand potential of a system of interacting electrons is considered as a stationary point of a self-energy functional. It is shown that a rigorous evaluation of the functional is possible for self-energies that are representable within a…
We present quadrature schemes to calculate matrices, where the so-called modified Hilbert transformation is involved. These matrices occur as temporal parts of Galerkin finite element discretizations of parabolic or hyperbolic problems when…
We propose a new, simple model-independent method to extract information of near-threshold resonances, such as complex energies and residues. The method is based on the observation that the Green's function and the T-matrix can be…
Local field correction effects on intra-layer inelastic scattering rate of interacting electrons are theoretically investigated in a coupled-quantum-wells structure, at finite temperature. At first, temperature dependent dynamic dielectric…
Hedin's scheme is solved with the inclusion of the vertex function ($GW\Gamma$) for a set of small molecules. The computational scheme allows for the consistent inclusion of the vertex both at the polarizability level and in the…
We study the extended Bose-Hubbard model on the square lattice at half filling as a function of next-nearest neighbor hopping amplitude and interaction strength. To variationally map out the phase diagram of this model, we develop a…