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Efficient thermoelectric materials are highly desirable, and the quest for finding them has intensified as they could be promising alternatives to fossil energy sources. Here we present a general first-principles approach to predict, in…
An O(N) algorithm is proposed for calculating linear response functions of non-interacting electrons in arbitray potential. This algorithm is based on numerical solution of the time-dependent Schroedinger equation discretized in space, and…
Different numerical approaches for the stray-field calculation in the context of micromagnetic simulations are investigated. We compare finite difference based fast Fourier transform methods, tensor grid methods and the finite-element…
We present a review of the basic ideas and techniques of the spectral density functional theory which are currently used in electronic structure calculations of strongly-correlated materials where the one-electron description breaks down.…
We present a spectrally accurate method for the rapid evaluation of free-space Stokes potentials, i.e. sums involving a large number of free space Green's functions. We consider sums involving stokeslets, stresslets and rotlets that appear…
We present a high-accuracy procedure for electronic structure calculations of strongly correlated materials. To address limitations in current electronic structure methods, we employ density functional theory in combination with the…
In this article, we present an $O(N \log N)$ rapidly convergent algorithm for the numerical approximation of the convolution integral with radially symmetric weakly singular kernels and compactly supported densities. To achieve the reduced…
Calculations of the two-loop electron self-energy for the $n = 1$ and $n = 2$ states of hydrogen-like ions are reported, performed to all orders in the nuclear binding strength parameter $Z\alpha$ (where $Z$ is the nuclear charge number and…
A novel low complexity method to perform self-consistent electronic-structure calculations using the Kohn-Sham formalism of density functional theory is presented. Localization constraints are neither imposed nor required thereby allowing…
The calculation of material phonon thermal conductivity from density functional theory calculations requires computationally expensive evaluation of anharmonic interatomic force constants and has remained a computational bottleneck in the…
Electronic Structure Theory (EST) describes the behavior of electrons in matter and is used to predict material properties. Conventionally, this involves forming a Hamiltonian and solving the Schr\"odinger equation through discrete…
This paper presents a quantum algorithm for efficiently computing partial sums and specific weighted partial sums of quantum state amplitudes. Computation of partial sums has important applications, including numerical integration,…
We present an efficient perturbative method to obtain both static and dynamic polarizabilities and hyperpolarizabilities of complex electronic systems. This approach is based on the solution of a frequency dependent Sternheimer equation,…
Linear scaling methods provide total energy, but no energy levels and canonical wavefuctions. From the density matrix computed through the density matrix purification methods, we propose an order-N (O(N)) method for calculating both the…
We present $\mathcal{O}(N^2)$ estimators for the small-scale power spectrum and bispectrum in cosmological simulations. In combination with traditional methods, these allow spectra to be efficiently computed across a vast range of scales,…
The method of McCurdy, Baertschy, and Rescigno, J. Phys. B, 37, R137 (2004) is generalized to obtain a straightforward, surprisingly accurate, and scalable numerical representation for calculating the electronic wave functions of molecules.…
Gaussian process (GP) emulator has been used as a surrogate model for predicting force field and molecular potential, to overcome the computational bottleneck of molecular dynamics simulation. Integrating both atomic force and energy in…
The best deterministic unconditionally proven integer factorization algorithms have exponential running time complexities of O(N^(1/4)) arithmetic operations, and conditional on the Riemann hypothesis, there is a deterministic algorithm of…
Quantum computers have the potential to efficiently solve a system of nonlinear ordinary differential equations (ODEs), which play a crucial role in various industries and scientific fields. However, it remains unclear which system of…
We introduce the notion of electronic enthalpy for first-principles structural and dynamical calculations of finite systems under pressure. An external pressure field is allowed to act directly on the electronic structure of the system…