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Quantization of electrodynamics in curved space-time in the Lorenz gauge and with arbitrary gauge parameter makes it necessary to study Green functions of non-minimal operators with variable coefficients. Starting from the integral…
We present a direct ab initio solution of the Schrodinger equation for neutral helium and helium-like atoms that reproduces the energy of the singlet S state 1S0. By redefining the two-electron wavefunction with tools from complex analysis…
This paper is devoted to the study and interpretation of the spectral function $\mathbf{A}(\omega, T)$ of the Keldysh nonequilibrium Green's function. The spatial diagonal of the spectral function is often interpreted as a time-dependent…
We present a numerically efficient technique to evaluate the Green's function for extended two dimensional systems without relying on periodic boundary conditions. Different regions of interest, or `patches', are connected using self energy…
A hyperbolic integro-differential equation is considered, as a model problem, where the convolution kernel is assumed to be either smooth or no worse than weakly singular. Well-posedness of the problem is studied in the context of semigroup…
This paper proposes a strong second-order two-step explicit/implicit technique with spectral orthogonal basis Galerkin finite element method for solving a two-dimensional Gray-Scott model subject to appropriate initial and boundary…
We present for static density functional theory and time-dependent density functional theory calculations an all-electron method which employs high-order hierarchical finite element bases. Our mesh generation scheme, in which structured…
In this paper, we present a mathematical analysis of time-dependent $N$-body electronic systems and establish mixed regularity for the corresponding wavefunctions. Based on this, we develop sparse grid approximations to reduce computational…
Precise algorithms capable of providing controlled solutions in the presence of strong interactions are transforming the landscape of quantum many-body physics. Particularly exciting breakthroughs are enabling the computation of non-zero…
We present a method to compute the many-body real-time Green's function using an adaptive variational quantum dynamics simulation approach. The real-time Green's function involves the time evolution of a quantum state with one additional…
Non equilibrium Green's function methods are regularly used to calculate current and charge densities in nanoscale (both molecular and semiconductor) conductors under bias. This method is mainly used for ballistic conduction but may be…
We present a microscopic modeling for a decay of a heavy compound nucleus, starting from a nucleonic degree of freedom. To this end, we develop an approach based on a non-equilibrium Green's function, which is combined with a configuration…
Modeling nanoscale devices quantum mechanically is a computationally challenging problem where new methods to solve the underlying equations are in a dire need. In this paper, we present an approach to calculate the charge density in…
We consider the cumulant expansion of the PAM employing the hybridization as perturbation (Phys. Rev. B 50, 17933 (1994)), and we obtain formally exact one-electron Green's functions (GF). These GF contain effective cumulants that are as…
Non-classical states are of practical interest in quantum computing and quantum metrology. These states can be detected through their Wigner function negativity in some regions. In this paper, we calculate the ground state of the…
We present two new developments for computing excited state energies within the $GW$ approximation. First, calculations of the Green's function and the screened Coulomb interaction are decomposed into two parts: one is deterministic while…
The technique of quantum electrodynamics (QED) calculations of energy levels in the helium atom is reviewed. The calculations start with the solution of the Schr\"odinger equation and account for relativistic and QED effects by perturbation…
A boundary integral equation method for the 3-D Helmholtz equation in multilayered media with many quasi-periodic layers is presented. Compared with conventional quasi-periodic Green's function method, the new method is robust at all…
A model is proposed to study the hybrid exciton in a quantum dot-dendrimer systems. The semiconductor organic hybrid exciton is studied using a "real space" Green's function method and a diagrammatic technique. The energy of the hybrid…
We provide a systematic approach to compute different kinds of non-equilibrium Green's functions for open quantum systems which are essentially two-point correlation functions in time. We reveal that the definition of Green's functions…