Related papers: Hyper-sparsity of the density matrix in a wavelet …
A density matrix describes the statistical state of a quantum system. It is a powerful formalism to represent both the quantum and classical uncertainty of quantum systems and to express different statistical operations such as measurement,…
We present a method to perform fully selfconsistent density-functional calculations, which scales linearly with the system size and which is well suited for very large systems. It uses strictly localized pseudoatomic orbitals as basis…
Fourier extension is an approximation method that alleviates the periodicity requirements of Fourier series and avoids the Gibbs phenomenon when approximating functions. We describe a similar extension approach using regular wavelet bases…
Methods exhibiting linear scaling with respect to the size of the system, so called O(N) methods, are an essential tool for the calculation of the electronic structure of large systems containing many atoms. They are based on algorithms…
A nearly optimal explicitly-sparse representation for oscillatory kernels is presented in this work by developing a curvelet based method. Multilevel curvelet-like functions are constructed as the transform of the original nodal basis. Then…
Anisotropic decompositions using representation systems such as curvelets, contourlet, or shearlets have recently attracted significantly increased attention due to the fact that they were shown to provide optimally sparse approximations of…
We present a generalization of the Li, Nunes and Vanderbilt density-matrix method to the case of a non-orthogonal set of basis functions. A representation of the real-space density matrix is chosen in such a way that only the overlap…
We describe recent progress in developing practical ab initio methods for which the computer effort is proportional to the number of atoms: linear scaling or O(N) methods. It is shown that the locality property of the density matrix gives a…
We present a detailed comparison between ONETEP, our linear-scaling density functional method, and the conventional pseudopotential plane wave approach in order to demonstrate its high accuracy. Further comparison with all-electron…
Diffuse atomic orbital basis sets have proven to be essential to obtain accurate interaction energies, especially in regard to non-covalent interactions. However, they also have a detrimental impact on the sparsity of the one-particle…
Using the finite Fourier transform, we introduce a generalization of Pauli-spin matrices for $d$-dimensional spaces, and the resulting set of unitary matrices $S(d) $ is a basis for $d\times d$ matrices. If $N=d_{1}\times…
The density matrix formalism which is widely used in the theory of measurements, quantum computing, quantum description of chemical and biological systems always imply the averaging over the states of the environment. In practice this is…
A finite dimensional quantum mechanical system is modeled by a density rho, a trace one, positive semi-definite matrix on a suitable tensor product space H[N] . For the system to demonstrate experimentally certain non-classical behavior,…
The past thirteen years have seen the development of many algorithms for approximating matrix functions in O(N) time, where N is the basis size. These O(N) algorithms rely on assumptions about the spatial locality of the matrix function;…
We consider the scattering matrices of massive quantum field theories with no bound states and a global $O(N)$ symmetry in two spacetime dimensions. In particular we explore the space of two-to-two S-matrices of particles of mass $m$…
The aperture mass statistic is a common tool used in weak lensing studies. By convolving lensing maps with a filter function of a specific scale, chosen to be larger than the scale on which the noise is dominant, the lensing signal may be…
We analyze the problem of determining the electronic ground state within O(N) schemes, focusing on methods in which the total energy is minimized with respect to the density matrix. We note that in such methods a crucially important…
The applications of machine learning techniques to chemistry and materials science become more numerous by the day. The main challenge is to devise representations of atomic systems that are at the same time complete and concise, so as to…
A quantum system's state is identified with a density matrix. Though their probabilistic interpretation is rooted in ensemble theory, density matrices embody a known shortcoming. They do not completely express an ensemble's physical…
In this article, we introduce the concept of samplets by transferring the construction of Tausch-White wavelets to the realm of data. This way we obtain a multilevel representation of discrete data which directly enables data compression,…