Related papers: Faster spectral density calculation using energy m…
Large scale Density Functional Theory (DFT) based electronic structure calculations are highly time consuming and scale poorly with system size. While semi-empirical approximations to DFT result in a reduction in computational time versus…
We describe a spectral method for the numerical solution of the Vlasov-Poisson system where the velocity space is decomposed by means of an Hermite basis, and the configuration space is discretized via a Fourier decomposition. The novelty…
Under the frequency domain framework for weakly dependent functional time series, a key element is the spectral density kernel which encapsulates the second-order dynamics of the process. We propose a class of spectral density kernel…
We present an efficient algorithm for the all-electron periodic Coulomb matrix based on the Ewald summation combined with the Fourier-transformed Coulomb method. The short-range contributions involving compact densities are evaluated in…
This chapter concerns with the recent development of a new DFT methodology for accurate, reliable prediction of many-electron systems. Background, need for such a scheme, major difficulties encountered, as well as their potential remedies…
The second in a two-part series, this paper extends the 3rd-order Spectral Representation Method for simulation of ergodic multi-variate stochastic processes according to a prescribed cross power spectral density and cross bispectral…
We present a novel nuclear energy density functional method to calculate spectroscopic properties of atomic nuclei. Intrinsic nuclear quadrupole deformations and rotational frequencies are considered simultaneously as the degrees of freedom…
X-ray absorption spectroscopy (XAS) is a leading technique for understanding structural changes in advanced battery materials such as lithium-excess cathodes. However, extracting critical information like oxidation states from the…
We introduce two efficient algorithms for computing the partial Fourier transforms in one and two dimensions. Our study is motivated by the wave extrapolation procedure in reflection seismology. In both algorithms, the main idea is to…
Simulating a Gaussian process requires sampling from a high-dimensional Gaussian distribution, which scales cubically with the number of sample locations. Spectral methods address this challenge by exploiting the Fourier representation,…
This algorithm is designed to perform numerical transforms to convert data from the temporal domain into the spectral domain. This algorithm obtains the spectral magnitude and phase by studying the Coefficient of Determination of a series…
We present a novel approach to the regression of quantum mechanical energies based on a scattering transform of an intermediate electron density representation. A scattering transform is a deep convolution network computed with a cascade of…
This paper introduces a generalised 3rd-order Spectral Representation Method for the simulation of multi-dimensional stochastic fields with asymmetric non-linearities. The simulated random fields satisfy a prescribed Power Spectrum and…
Three-centre nuclear attraction integrals, which arise in density functional and \textit{ab initio} calculations, are one of the most time-consuming computations involved in molecular electronic structure calculations. Even for relatively…
The most advanced techniques using fault-tolerant quantum computers to estimate the ground-state energy of a chemical Hamiltonian involve compression of the Coulomb operator through tensor factorizations, enabling efficient block-encodings…
The accurate computation of low-energy spectra of strongly correlated quantum many-body systems, typically accessed via Green's-functions, is a long-standing problem posing enormous challenges to numerical methods. When the spectral…
We introduce a nonparametric spectral density estimator for continuous-time and continuous-space processes measured at fully irregular locations. Our estimator is constructed using a weighted nonuniform Fourier sum whose weights yield a…
The complex Fourier transform of the two-point correlator of the energy spectrum of a quantum system is known as the spectral form factor (SFF). It constitutes an essential diagnostic tool for phases of matter and quantum chaos. In black…
A method for beyond-mean-field calculations based on an energy density functional is described. The main idea is to map the energy surface for the nuclear quadrupole deformation, obtained from an energy density functional at the mean-field…
We develop an approach to spectral estimation that has been advocated by Ferrante, Masiero and Pavon and, in the context of the scalar-valued covariance extension problem, by Enqvist and Karlsson. The aim is to determine the power spectrum…