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The quantum models of a massive scalar particle inside of an open bag generated by a pseudo-Gaussian conformaly flat (1+1) metrics are investigated. The potential of a free moving test particle, in the generated metric, has Gaussian…
We present GPU implementations of two fast force calculation methods, based on series expansions of the Poisson equation. One is the Self-Consistent Field (SCF) method, which is a Fourier-like expansion of the density field in some basis…
The cumulant expansion of the Green's function is a computationally efficient beyond-$GW$ approach renowned for its significant enhancement of satellite features in materials. In contrast to the ubiquitous $GW$ approximation of many-body…
Using contiguous relations we construct an infinite number of continued fraction expansions for ratios of generalized hypergeometric series 3F2(1). We establish exact error term estimates for their approximants and prove their rapid…
The Gaussian beam superposition method is an asymptotic method for computing high frequency wave fields in smoothly varying inhomogeneous media. In this paper we study the accuracy of the Gaussian beam superposition method and derive error…
Self-consistent field theory (SCFT) is one of the useful methods to simulate phase separated structures of multi-component polymer systems. In this article, we propose an SCFT for semiflexible polymer melts, where the basic equations for…
Using an algebraic Fourier transform of operators, we develop a method (F-method) to obtain explicit highest weight vectors in the branching laws by differential equations. This article gives a brief explanation of the F-method and its…
Free energy landscapes provide insights into conformational ensembles of biomolecules. In order to analyze these landscapes and elucidate mechanisms underlying conformational changes, there is a need to extract metastable states with…
A new finite element method with discontinuous approximation is introduced for solving second order elliptic problem. Since this method combines the features of both conforming finite element method and discontinuous Galerkin (DG) method,…
Highly accurate nonrelativistic ground-state wave function and energy of the lithium atom is obtained in the Hylleraas basis set. The leading relativistic corrections,as represented by Breit-Pauli Hamiltonian, are obtained in fair agreement…
The accuracy of Green Function Monte Carlo (GFMC) simulations can be greatly improved by a clever choice of the approximate ground state wave function that controls configuration sampling. This trial wave function typically depends on many…
Defects in conformal field theories are interesting objects to study from both formal and applied points of view. In this paper, we construct conformal defects in free scalar field CFTs in diverse dimensions. After discussing the possible…
In this paper we show that a methodology based on a sampling with the Gaussian function of kind $h\,{e^{ - {{\left( {t/c} \right)}^2}}}/\left( {{c}\sqrt \pi } \right)$, where ${c}$ and $h$ are some constants, leads to the Fourier transform…
We implement the phaseless auxiliary field quantum Monte Carlo method using the plane-wave based projector augmented wave method and explore the accuracy and the feasibility of applying our implementation to solids. We use a singular value…
This paper introduces a method for computing the Helmholtz free energy using the flow matching technique. Unlike previous work that utilized flow-based models for variational free energy calculations, this method provides bounds for free…
Deriving from the gradient vector of a generative model of local features, Fisher vector coding (FVC) has been identified as an effective coding method for image classification. Most, if not all, FVC implementations employ the Gaussian…
We adopt the frozen Gaussian approximation (FGA) for modeling seismic waves. The method belongs to the category of ray-based beam methods. It decomposes seismic wavefield into a set of Gaussian functions and propagates these Gaussian…
Orbital-free density functional theory as an extension of traditional Thomas-Fermi theory has attracted a lot of interest in the past decade because of developments in both more accurate kinetic energy functionals and highly efficient…
We introduce a mixed density fitting scheme that uses both a Gaussian and a plane-wave fitting basis to accurately evaluate electron repulsion integrals in crystalline systems. We use this scheme to enable efficient all-electron Gaussian…
Fourier continuation is an approach used to create periodic extensions of non-periodic functions in order to obtain highly-accurate Fourier expansions. These methods have been used in PDE-solvers and have demonstrated high-order convergence…