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We unearth the interconnection between various analytical methods which are widely used in the current literature to identify integrable nonlinear dynamical systems described by third-order nonlinear ordinary differentiable equations…
A complete discrete set of spherical single-particle wave functions for studies of weakly-bound many-body systems is proposed. The new basis is obtained by means of a local-scale point transformation of the spherical harmonic oscillator…
Attaining a reliable complete basis set (CBS) limit remains a significant challenge in ab initio correlated electronic-structure calculations. Building on our previous work for atoms and diatomic molecules, we present a finite-element (FE)…
We propose a method based on sinc series approximations for computing the Rayleigh-Sommerfeld and Fresnel diffraction integrals of optics. The diffraction integrals are given in terms of a convolution, and our proposed numerical approach is…
The description of realistic strongly correlated systems has recently advanced through the combination of density functional theory in the local density approximation (LDA) and dynamical mean field theory (DMFT). This LDA+DMFT method is…
In part I we introduced modified Landweber-Kaczmarz methods and have established a convergence analysis. In the present work we investigate three applications: an inverse problem related to thermoacoustic tomography, a nonlinear inverse…
An extension of the Kramers-Kronig method for treatment of polarized infrared reflectance spectra from the face of low-symmetry crystals, where directions of principal dielectric axes depend on frequency, is proposed. It is shown, how to…
Given the widespread use of density functional theory (DFT), there is an increasing need for the ability to model large systems (beyond 1,000 atoms). We present a brief overview of the large-scale DFT code Conquest, which is capable of…
Linear scaling density functional theory approaches to electronic structure are often based on the tendency of electrons to localize even in large atomic and molecular systems. However, in many cases of actual interest, for example in…
We introduce a diagrammatic quantum field formalism for the evaluation of normalized expectation values of operators, and suitable for systems with localized electrons. It is used to develop a convergent series expansion for the energy in…
Conventional optical components have been proposed to realize high-quality line focusing with uniform intensity distribution such as cylindrical lenses, segmented wedge-arrays, or a combination of prisms and spherical mirrors. However,…
A novel Gaussian-Sinc mixed basis set for the calculation of the one-electron electronic structure within a uniform magnetic field in three dimensions is presented. The one-electron system is used to demonstrate the utility of this new…
In the context of photoelectron spectroscopy, the $GW$ approach has developed into the method of choice for computing excitation spectra of weakly correlated bulk systems and their surfaces. To employ the established computational schemes…
Quantum--Mechanical methods that are both computationally fast and accurate are not yet available for electronic excitations having charge transfer character. In this work, we present a significant step forward towards this goal for those…
We study the position estimation of a mechanical oscillator undergoing both detuned parametric amplification and continuous quantum measurement. This model, which can be utilised to produce squeezed states, is applied to a general…
In this document, we briefly review the two-electron integral algorithms based on the range-separated algorithms and Fourier transform integral algorithms that are implement ed in the PySCF package. For each integral algorithm, we estimate…
In this work we analyze the complex scaling method applied to the problem of time-harmonic scalar wave propagation in junctions between `leaky,' or open dielectric waveguides. In [arXiv:2302.04353, arXiv:2310.05816, arXiv:2401.04674,…
The electronic spectra of light one-electron quasi-molecular compounds H-H$^+$, He$^+$-He$^2+$ and He$^+$-H$^+$ are analyzed. To this end, the two-center Dirac equation is solved by the dual-kinetically balanced finite-basis-set method for…
This is the second of two papers which address the problem of measuring the unredshifted power spectrum of fluctuations from a galaxy survey in optimal fashion. A key quantity is the Fisher matrix, which is the inverse of the covariance…
The 3-d inverse scattering problem of the reconstruction of the unknown dielectric permittivity in the generalized Helmholtz equation is considered. The main difference with the conventional inverse scattering problems is that only the…