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We applied localized orbital scaling correction (LOSC) in Bethe-Salpeter equation (BSE) to predict accurate excitation energies for molecules. LOSC systematically eliminates the delocalization error in the density functional approximation…
The $\Sigma$-method for structural analysis of a differential-algebraic equation (DAE) system produces offset vectors from which the sparsity pattern of DAE's system Jacobian is derived; this pattern implies a fine block-triangular form…
We propose Noise-Based Spectral Embedding (NBSE), a physics-informed framework for selecting informative features from high-dimensional data without greedy search. NBSE constructs a sparse similarity graph on the samples and identifies the…
In this article, we present an interpolative separable density fitting (ISDF) based algorithm to calculate exact exchange in periodic mean field calculations. In the past, decomposing the two-electron integrals into tensor hypercontraction…
The Immersed Boundary method is a simple, efficient, and robust numerical scheme for solving PDE in general domains, yet it only achieves first-order spatial accuracy near embedded boundaries. In this paper, we introduce a new high-order…
The quasiparticle electronic structure and optical excitation of anatase TiO$_2$ is determined within the framework of many-body perturbation theory (MBPT) by combining the $G_0W_0$ method and the Bethe-Salpeter Equation (BSE). A modified…
Resonant absorption imaging is a common technique for detecting the two-dimensional column density of ultracold atom systems. In many cases, the system's thickness along the imaging direction greatly exceeds the imaging system's depth of…
Despite advancements in electron backscatter diffraction (EBSD) detector speeds, the acquisition rates of 4-Dimensional (4D) EBSD data, i.e., a collection of 2-dimensional (2D) diffraction maps for every position of a convergent electron…
We present a molecular extension of our recently proposed Green's function embedding method, interacting-bath dynamical embedding theory (ibDET), for computing charged excitation energies at the $GW$ and EOM-CCSD levels. Starting from…
X-ray photoelectron spectroscopy (XPS) measures core-electron binding energies (CEBEs) to reveal element-specific insights into chemical environment and bonding. Accurate theoretical CEBE prediction aids XPS interpretation but requires…
The lowest electronic excitations of benzene and a set of donor-acceptor molecular complexes are calculated for the gas phase and on the Al(111) surface using the many-body Bethe-Salpeter equation (BSE). The energy of the charge-transfer…
The one-dimensional asymmetric simple exclusion process (ASEP), where $N$ hard-core particles hop forward with rate $1$ and backward with rate $q<1$, is considered on a periodic lattice of $L$ site. Using KPZ universality and previous…
A new method for calculating optical absorption spectra within linear-scaling density-functional theory (LS-DFT) is presented, incorporating a scheme for optimizing a set of localized orbitals to accurately represent unoccupied Kohn-Sham…
This paper introduces a new approximation scheme for solving high-dimensional semilinear partial differential equations (PDEs) and backward stochastic differential equations (BSDEs). First, we decompose a target semilinear PDE (BSDE) into…
In order to solve the Bethe-Salpeter equation (BSE) in the Minkowski space, we first introduce the Nakanishi integral representations of the Bethe-Salpeter amplitude (BSA) and the Bethe-Salpeter wave function (BSWF). We then derive the…
We present a first-principles method for relaxing a material's geometry in an optically excited state. This method, based on the Bethe-Salpeter equation, consists of solving coupled equations for exciton wavefunctions and atomic…
In this paper we propose a new sampling-free approach to solve Bayesian model inversion problems that is an extension of the previously proposed spectral likelihood expansions (SLE) method. Our approach, called stochastic spectral…
We develop a fast and scalable computational framework to solve large-scale and high-dimensional Bayesian optimal experimental design problems. In particular, we consider the problem of optimal observation sensor placement for Bayesian…
An ab initio approach is presented for studying the collective excitations in excitonic insulators, charge/spin density waves and superconductors. We derive the Bethe-Salpeter-Equation for the particle-hole excitations in the quasiparticle…
We formulate an ab initio downfolding scheme for electron-phonon coupled systems. In this scheme, we calculate partially renormalized phonon frequencies and electron-phonon coupling, which include the screening effects of high-energy…