Related papers: Real-Space Spectral Approach to Orbital Magnetizat…
Orbital magnetization, a key property arising from the orbital motion of electrons, plays a crucial role in determining the magnetic behavior of molecules and solids. Despite its straightforward calculation in finite systems, the…
Accurate calculations of the spectral density in a strongly correlated quantum many-body system are of fundamental importance to study its dynamics in the linear response regime. Typical examples are the calculation of inclusive and…
We have extended the spectral dynamics formalism introduced by Binney & Spergel, and have implemented a semi-analytic method to represent regular orbits in any potential, making full use of their regularity. We use the spectral analysis…
We demonstrate the power of a first principle-based and practicable method that allows for the perturbative computation of reduced density matrix elements of an open quantum system without making use of any master equations. The approach is…
We derive macroscopic expressions for the polarization and orbital magnetization of a Chern insulator in its zero-temperature ground state using a previously developed formalism for treating microscopic polarization and magnetization fields…
The Stark resonance parameters for the $3a_{1}$ molecular orbital of H$_{2}$O are computed by solving a system of partial differential equations in spherical polar coordinates. The starting point of the calculation is the quantum potential…
The procedure for simulating the nuclear magnetic resonance spectrum linked to the spin system of a molecule for a certain nucleus entails diagonalizing the associated Hamiltonian matrix. As the dimensions of said matrix grow exponentially…
A direct orbital optimization method is presented for density functional calculations of excited electronic states using either a real space grid or a plane wave basis set. The method is variational, provides atomic forces in the excited…
We develop a sparse spectral method for a class of fractional differential equations, posed on $\mathbb{R}$, in one dimension. These equations can include sqrt-Laplacian, Hilbert, derivative and identity terms. The numerical method utilizes…
In a recent paper we have suggested that the finite temperature density matrix can be computed efficiently by a combination of polynomial expansion and iterative inversion techniques. We present here significant improvements over this…
The complex-scaling method can be used to calculate molecular resonances within the Born-Oppenheimer approximation, assuming the electronic coordinates are dilated independently of the nuclear coordinates. With this method, one will…
We derive full-sky, real-space operators that convert between polarization Stokes Q/U parameters and the coordinate-independent scalar E/B modes that are widely used in Cosmic Microwave Background (CMB) and cosmic shear analysis. We also…
In this article, we study numerical approximation of eigenvalue problems of the Schr\"{o}dinger operator $\displaystyle -\Delta u + \frac{c^2}{|x|^2}u$. There are three stages in our investigation: We start from a ball of any dimension, in…
Magneto-optical response, i.e. optical response in the presence of a magnetic field, is commonly used for characterization of materials and in optical communications. However, quantum mechanical description of electric and magnetic fields…
Electrons in moir\'e flat band systems can spontaneously break time reversal symmetry, giving rise to a quantized anomalous Hall effect. Here we use a superconducting quantum interference device to image stray magnetic fields in one such…
We present a novel spectral solver for general relativistic magnetohydrodynamics on dynamical spacetimes. By combining a high order discontinuous spectral method on mapped Chebyshev Fourier grids, our scheme attains exponential convergence.…
We introduce a practical and efficient approach for calculating the all-electron full potential bandstructure in real space, employing a finite element basis. As an alternative to the k-space method, the method involves the self-consistent…
In the real space formalism of orbital magnetization (OM) for a Chern insulator without an external electric field, it is correct to average the local OM either over the bulk region or over the whole sample. However for a layered Chern…
A spectral element method (SEM) is developed to solve polarized radiative transfer in multidimensional participating medium. The angular discretization is based on the discrete-ordinates approach, and the spatial discretization is conducted…
The determination of the energy spectra of small spin systems as for instance given by magnetic molecules is a demanding numerical problem. In this work we review numerical approaches to diagonalize the Heisenberg Hamiltonian that employ…