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The quantum many-electron problem is not just at the heart of condensed matter phenomena, but also essential for first-principles simulation of chemical phenomena. Strong correlation in chemical systems are prevalent and present a…

First principles calculations based on density functional theory are having an incerasing impact on our understanding of molecule-surface interactions. For example, calculations of the multi-dimensional potential energy surface have…

We study a generalization of the Gaussian effective potential for self-interacting scalar fields in one and two spatial dimensions. We compute the two-loop corrections and discuss the renormalization of the generalized Gaussian effective…

We have focused on Answer Set Programming (ASP), more specifically, answer set counting, exploring both exact and approximate methodologies. We developed an exact ASP counter, sharpASP, which utilizes a compact encoding for propositional…

For nonsupersymmetric theories, the one-loop effective action can be computed via zeta function regularization in terms of the functional trace of the heat kernel associated with the operator which appears in the quadratic part of the…

Evaluation of basic integrals over Gaussian functions, traditionally utilized for electronic structure computations on molecules and solids, is discussed in a pedagogical form.

Learning PDE dynamics for fluids increasingly relies on neural operators and Transformer-based models, yet these approaches often lack interpretability and struggle with localized, high-frequency structures while incurring quadratic cost in…

We propose a computational method that simplifies drastically the inclusion of spin-orbit interaction in density functional theory implemented on localised atomic orbital basis sets. Our method is based on a well-known procedure for…

A particle-in-cell algorithm is derived with a canonical Poisson structure in the formalism of finite element exterior calculus. The resulting method belongs to the class of gauge-compatible splitting algorithms, which exactly preserve…

Over the past 10 years Bayesian methods have rapidly grown more popular as several computationally intensive statistical algorithms have become feasible with increased computer power. In this paper, we begin with a general description of…

We present an analysis of different methods to calculate the classical electrostatic Hartree potential created by charge distributions. Our goal is to provide the reader with an estimation on the performance ---in terms of both numerical…

A review of methods for finding general expressions for matrix elements (non-diagonal with respect to configurations included) of any one- and two-particle operator for an arbitrary number of shells in an atomic configuration is given.…

Computing the posterior distribution of a probabilistic program is a hard task for which no one-fit-for-all solution exists. We propose Gaussian Semantics, which approximates the exact probabilistic semantics of a bounded program by means…

The total energies and the spin states for atoms and their first ions with Z = 1-86 are calculated within the the local spin-density approximation (LSDA) and the generalized-gradient approximation (GGA) to the exchange-correlation (xc)…

In a recently developed approximation technique for quantum field theory the standard one-loop result is used as a seed for a recursive formula that gives a sequence of improved Gaussian approximations for the generating functional. In this…

Large-scale atomistic simulations rely on interatomic potentials providing an efficient representation of atomic energies and forces. Modern machine-learning (ML) potentials provide the most precise representation compared to electronic…

We derive an analytic connection between the screened self-consistent effective potential from density functional theory (DFT) and atomic effective pseudopotentials (AEPs). The motivation to derive AEPs is to address structures with…

Adaptive precision molecular dynamics simulations have developed along energy- and force-coupling approaches, which allow for a continuous transition between different particle descriptions or interaction potentials. Most approaches…

We utilize the combination of two standard trapping techniques, a magnetic trap and an optical trap in a Raman setup, to propose a versatile and tunable trap for cold atoms. The created potential provides several advantages over…

We show that a Gaussian Process model can be combined with a small number (of order 100) of scattering calculations to provide a multi-dimensional dependence of scattering observables on the experimentally controllable parameters such as…