Related papers: Inferring crystal electronic properties from exper…
The one-body reduced density matrix (1-RDM) of a many-body system at zero temperature gives direct access to many observables, such as the charge density, kinetic energy and occupation numbers. It would be desirable to express it as a…
We present a method that calibrates a semi-analytic model to the Renaissance Simulations, a suite of cosmological hydrodynamical simulations with high-redshift galaxy formation. This approach combines the strengths of semi-analytic…
In a recent article (Canc\`es, Deleurence and Lewin, Commun. Math. Phys., 281 (2008), pp. 129-177), we have rigorously derived, by means of bulk limit arguments, a new variational model to describe the electronic ground state of insulating…
A simple model of 1D structure based on a Fibonacci sequence with variable atomic spacings is proposed. The model allows for observation of the continuous transition between periodic and non-periodic diffraction patterns. The diffraction…
When a sample's X-ray diffraction pattern (XRD) is measured, the corresponding crystal structure is usually determined by searching for similar XRD patterns in the database. However, if a similar XRD pattern is not found, it is tremendously…
Hubertus J. J. van Dam [Phys. Rev. A 93, 052512, 2016] claims that the one-particle reduced density matrix (1RDM) of an interacting system can be represented by means of a single-determinant wavefunction of fictitious non-interacting…
X-ray crystallography (XC) is an experimental technique used to determine three-dimensional crystalline structures. The acquired data in XC, called diffraction patterns, is the Fourier magnitudes of the unknown crystalline structure. To…
A simple expression is derived for the band structure of a one-dimensional periodic potential in terms of two solutions of the Schroedinger equation within the unit cell, one with a zero-derivative boundary condition on the left-hand end of…
Numerical simulations of crystal defects are necessarily restricted to finite computational domains, supplying artificial boundary conditions that emulate the effect of embedding the defect in an effectively infinite crystalline…
In this article we consider the widely used immersed finite element method (IFEM), in both explicit and implicit form, and its relationship to our more recent one-field fictitious domain method (FDM). We review and extend the formulation of…
A Python program for calculating the metrics necessary to perform information-theory based symmetry classifications and quantifications of transmission electron diffraction spot patterns is introduced. It is the first of its kind, in that…
One of the long-standing problems in materials science is how to predict a material's structure and then its properties given only its composition. Experimental characterization of crystal structures has been widely used for structure…
Machine learning (ML) is widely used to explore crystal materials and predict their properties. However, the training is time-consuming for deep-learning models, and the regression process is a black box that is hard to interpret. Also, the…
We present randomized algorithms for estimating the trace and deter- minant of Hermitian positive semi-definite matrices. The algorithms are based on subspace iteration, and access the matrix only through matrix vector products. We analyse…
In machine learning or statistics, it is often desirable to reduce the dimensionality of a sample of data points in a high dimensional space $\mathbb{R}^d$. This paper introduces a dimensionality reduction method where the embedding…
For many-electron systems, the second-order reduced density matrix (2-RDM) provides sufficient information for characterizing their properties of interests in physics and chemistry, ranging from total energy, magnetism, quantum correlation…
In this paper, based on the analysis of the formula (2.2) for calculating the elastic scattering diagrams of microparticles on a multilayer crystal surface, derived by the author in the article [3], it is shown that the stochastic approach…
Recent results in compressed sensing show that, under certain conditions, the sparsest solution to an underdetermined set of linear equations can be recovered by solving a linear program. These results either rely on computing sparse…
Computational methods that automatically extract knowledge from data are critical for enabling data-driven materials science. A reliable identification of lattice symmetry is a crucial first step for materials characterization and…
Crystal structures are characterized by atomic bases within a primitive unit cell that repeats along a regular lattice throughout 3D space. The periodic and infinite nature of crystals poses unique challenges for geometric graph…