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The performance of basis sets made of numerical atomic orbitals is explored in density-functional calculations of solids and molecules. With the aim of optimizing basis quality while maintaining strict localization of the orbitals, as…

An alternative parameterization of R-matrix theory is presented which is mathematically equivalent to the standard approach, but possesses features which simplify the fitting of experimental data. In particular there are no level shifts and…

The existing doubling algorithms have been proven efficient for several important nonlinear matrix equations arising from real-world engineering applications. In a nutshell, the algorithms iteratively compute a basis matrix, in one of the…

A recursive calculational scheme is developed for matrix elements in the generalized seniority scheme for the nuclear shell model. Recurrence relations are derived which permit straightforward and efficient computation of matrix elements of…

The many-body dispersion (MBD) framework is a successful approach for modeling the long-range electronic correlation energy and optical response of systems with thousands of atoms. Inspired by field theory, here we develop a…

One of the great challenges of modern science is to faithfully model, and understand, matter at a wide range of scales. Starting with atoms, the vastness of the space of possible configurations poses a formidable challenge to any simulation…

Given labeled data represented by a binary matrix, we consider the task to derive a Boolean matrix factorization which identifies commonalities and specifications among the classes. While existing works focus on rank-one factorizations…

We consider the quantum Toda chain using the method of separation of variables. We show that the matrix elements of operators in the model are written in terms of finite number of ``deformed Abelian integrals''. The properties of these…

Accurate simulations of atomistic systems from first principles are limited by computational cost. In high-throughput settings, machine learning can reduce these costs significantly by accurately interpolating between reference…

Joint diagonalization, the process of finding a shared set of approximate eigenvectors for a collection of matrices, arises in diverse applications such as multidimensional harmonic analysis or quantum information theory. This task is…

We develop a method to entangle neutral atoms using cold controlled collisions. We analyze this method in two particular set-ups: optical lattices and magnetic micro-traps. Both offer the possibility of performing certain multi-particle…

Classical atomistic simulations based on interatomic potentials resolve lattice instabilities, defect nucleation, and microstructure evolution with high fidelity, but their accessible system sizes remain far below those required for…

The central object of the quantum algebraic approach to the study of quantum integrable models is the universal $R$-matrix, which is an element of a completed tensor product of two copies of quantum algebra. Various integrability objects…

It is shown that quantization of the dynamical systems with second class constraints actually can be reduced to quantization of the systems with first class constraints. The motion of the non-relativistic particle along the plane curve and…

We prove the decomposition of arbitrary diagonal operators into tensor and matrix products of smaller matrices, focusing on the analytic structure of the resulting formulas and their inherent symmetries. Diagrammatic representations are…

Matrix elements between nonorthogonal Slater determinants represent an essential component of many emerging electronic structure methods. However, evaluating nonorthogonal matrix elements is conceptually and computationally harder then…

A model operator approach to calculations of the QED corrections to energy levels in relativistic many-electron atomic systems is developed. The model Lamb shift operator is represented by a sum of local and nonlocal potentials which are…

General approach to the multiplication or adjoint operation of $2\times 2$ block operator matrices with unbounded entries are founded. Furthermore, criteria for self-adjointness of block operator matrices based on their entry operators are…

An algebraic method for evaluating bare nucleon matrix elements of quark operators is proposed. Thereby, bare nucleon matrix elements are traced back to vacuum matrix elements. The method is similar to the soft pion theorem. Matrix elements…

The feasibility of shell-model calculations is radically extended by the Quantum Monte Carlo Diagonalization method with various essential improvements. The major improvements are made in the sampling for the generation of shell-model basis…