Related papers: Deflation algorithm for the Green function of quas…
A One-Dimensional (1D) Reduced-Order Model (ROM) has been developed for a 3D Rayleigh-B\'enard convection system in the turbulent regime with Rayleigh number $\mathrm{Ra}=10^6$. The state vector of the 1D ROM is horizontally averaged…
Joint diagonalization, the process of finding a shared set of approximate eigenvectors for a collection of matrices, arises in diverse applications such as multidimensional harmonic analysis or quantum information theory. This task is…
In this paper, new representations of the Green's function for an acoustic d-dimensional half-space problem with impedance boundary conditions are presented. The main features of the new representation are: a) in addition to additive terms…
We show that a classical algorithm efficiently simulating the modular exponentiation circuit, for certain product state input and with measurements in a general product state basis at the output, can efficiently simulate Shor's factoring…
A new method is presented for Fourier decomposition of the Helmholtz Green Function in cylindrical coordinates, which is equivalent to obtaining the solution of the Helmholtz equation for a general ring source. The Fourier coefficients of…
Diagrammatic analysis for normal state of Hubbard model proposed in our previous paper [1] is generalized and used to investigate superconducting state of this model. We use the notion of charge quantum number to describe the irreducible…
Applications of the H\"uckel (tight binding) model are ubiquitous in quantum chemistry and solid state physics. The matrix representation of this model is isomorphic to an unoriented vertex adjacency matrix of a bipartite graph, which is…
In this work, the low rank approximation concept is extended to the non-equilibrium Green's function (NEGF) method to achieve a very efficient approximated algorithm for coherent and incoherent electron transport. This new method is applied…
We present a combination method based on orignal version of Davidson algorithm for extracting few of the lowest eigenvalues and eigenvectors of a sparse symmetric Hamiltonian matrix and the simplest version of Lanczos technique for…
A number of elegant approaches have been developed for the identification of quantum circuits which can be efficiently simulated on a classical computer. Recently, these methods have been employed to demonstrate the classical simulability…
The method of the quasiclassical Green's function is used to determine the equilibrium properties of one-dimensional (1D) interacting Fermi systems, in particular, the bulk and the local (near a hard wall) density of states. While this is a…
Stationary electric transport in semiconductor nanostructures is studied by the method of nonequilibrium Green functions. In the case of sequential tunneling the results are compared with density matrix theory, providing almost identical…
Since the initial development of one-dimensional electron gases (1DEG) two decades ago, there has been intense interest in both the fundamental physics and the potential applications, including quantum computation, of these quantum…
In this work, we propose an efficient computational scheme for first-principle quantum transport simulations to evaluate the open-boundary conditions. Its partitioning differentiates from conventional methods in that the contact self-energy…
The Wave Function Matching (WFM) technique has recently been developed for the calculation of electronic transport in quantum two-probe systems. In terms of efficiency it is comparable with the widely used Green's function approach. The WFM…
Inverse design enables automating the discovery and optimization of devices achieving performance significantly exceeding that of traditional human-engineered designs. However, existing methodologies to inverse-design electromagnetic…
We show that Green function methods can be straightforwardly applied to nonlinear equations appearing as the leading order of a short time expansion. Higher order corrections can be then computed giving a satisfactory agreement with…
The evaluation of elastodynamic Green's functions across numerous source-receiver locations, frequencies, and material properties, particularly in the context of parametric studies or boundary element computations, is computationally…
We develop a non-overlapping domain decomposition method (DDM) for scalar wave scattering by periodic layered media. Our approach relies on robust boundary-integral equation formulations of Robin-to-Robin (RtR) maps throughout the frequency…
We propose an efficient procedure to obtain Green's functions by combining the shifted conjugate orthogonal conjugate gradient (shifted COCG) method with the nonequilibrium Green's function (NEGF) method based on a real-space…