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Linus Pauling contributions span structural biology, chemistry in its broadest definition, quantum mechanical theory, valence bond theory, and even nuclear physics. A principal tool developed and used by Pauling is Xray, and electron,…
An algorithm for determining crystal structures from diffraction data is described which does not rely on the usual Fourier-space formulations of atomicity. The new algorithm implements atomicity constraints in real-space, as well as…
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…
Recently, a new approach for solving the three-body problem for (d,p) reactions in the Coulomb-distorted basis in momentum space was proposed. Important input quantities for such calculations are the scattering matrix elements for proton-…
Under the name prime decomposition (pd), a unique decomposition of an arbitrary $N$-dimensional density matrix $\rho$ into a sum of seperable density matrices with dimensions given by the coprime factors of $N$ is introduced. For a class of…
The quantum deformation $CP_q(N)$ of complex projective space is discussed. Many of the features present in the case of the quantum sphere can be extended. The differential and integral calculus is studied and $CP_q(N)$ appears as a quantum…
The mechanism of describing quantum states by standard probability (tomographic one) instead of wave function or density matrix is elucidated. Quantum tomography is formulated in an abstract Hilbert space framework, by means of the identity…
To a representation of $\O_N$ (the Cuntz algebra with $N$ generators) we associate a projection valued measure and we study the case when this measure has atoms. The main technical tool are the spaces invariant for all the operators…
This work shows an approach to reduce the dimensionality of matrix representations of quantum channels. It is achieved by finding a base of the cone of positive semidefinite matrices which represent quantum channels. Next, this is…
The relation between the R- and P-matrix approaches and the harmonic oscillator representation of the quantum scattering theory (J-matrix method) is discussed. We construct a discrete analogue of the P-matrix that is shown to be equivalent…
The N-representability problem for reduced density matrices remains a fundamental challenge in electronic structure theory. Following our previous work that employs a unitary-evolution algorithm based on an adaptive derivative-assembled…
The quantum separability problem consists in deciding whether a bipartite density matrix is entangled or separable. In this work, we propose a machine learning pipeline for finding approximate solutions for this NP-hard problem in…
Matrices of the irreducible representations of double crystallographic point groups O, Td, Ox{1,I} and Tdx{1,I} are derived. The characteristic polynomials (spinor bases) up to the sixth power are obtained. The method for the derivation of…
The influence of non-uniform distribution of nuclei on crystallization kinetics of amorphous materials is investigated. This case cannot be described by the well-known Johnson-Mehl-Avrami (JMA) equation, which is only valid under the…
The purpose of this paper is to present an interpretation for the decomposition of the tensor product of two or more irreducible representations of GL(N) in terms of a system of quantum particles. Our approach is based on a certain…
The many-identical-particle quantum correlations are revisited utilizing the machinery of basic group theory, especially that of the group of permutations. It is done with the purpose to obtain precise definitions of effective distinct…
Density based representations of atomic environments that are invariant under Euclidean symmetries have become a widely used tool in the machine learning of interatomic potentials, broader data-driven atomistic modelling and the…
The N-representability problem consists in determining whether, for a given p-body matrix, there exists at least one N-body density matrix from which the p-body matrix can be obtained by contraction, that is, if the given matrix is a p-body…
An analytic proof is given of the necessity of the Borland-Dennis conditions for 3-representability of a one particle density matrix with rank 6. This may shed some light on Klyachko's recent use of Schubert calculus to find general…
Quantum gates and simple quantum algorithms can be designed utilizing the diffraction phenomena of a photon within a multiplexed holographic element. The quantum eigenstates we use are the photon's linear momentum (LM) as measured by the…