Related papers: Construction of Wannier Functions in Disordered Sy…
At short distances, energy eigenfunctions of chaotic systems have spatial correlations that are well described by assuming a microcanonical density in phase space for the corresponding Wigner function. However, this is not correct on large…
The momentum-space derivatives of Bloch wavefunctions are essential for studying quantum geometry and the equilibrium and response properties of solids. In practical first-principles calculations, these derivatives are obtained via Wannier…
This paper contains a brief sketch of some methods that can be used to obtain the Wigner function for a number of systems. We give an overview of the technique as it is applied to some simple differential systems related to diffusion…
We report one algorithm for simulating oxygen $K$-edge RIXS for weakly correlated systems, using maximally localized Wannier functions as the basis set. The $N$-electron wavefunction is formulated using the single Slater determinant, and…
In this paper, a gradient flow model is proposed for conducting ground state calculations in Wigner formalism of many-body system in the framework of density functional theory. More specifically, an energy functional for the ground state in…
Based on a functional-integral formalism, a generalization of the self-energy-functional theory (SFT) is proposed which is applicable to systems of interacting electrons with disorder. Similar to the pure case without disorder, a…
We obtain analytically a continuum of one-dimensional ballistic extended states in a two-dimensional disordered system, which consists of compactly coupled random and pure square lattices. The extended states give a marginal metallic phase…
In principle, density functional theory yields the correct ground-state densities and energies of electronic systems under the action of a static external potential. However, traditional approximations fail to include Van der Waals energies…
The Anderson model for independent electrons in a disordered potential is transformed analytically and exactly to a basis of random extended states leading to a variant of augmented space. In addition to the widely-accepted phase diagrams…
We present a semiclassical approach to eigenfunction statistics in chaotic and weakly disordered quantum systems which goes beyond Random Matrix Theory, supersymmetry techniques, and existing semiclassical methods. The approach is based on…
Many systems occurring in real-world applications, such as controlling the motions of robots or modeling the spread of diseases, are switched impulsive systems. To ensure that the system state stays in a safe region (e.g., to avoid…
In this work we study the Wigner functions, which are the quantum analogues of the classical phase space density, and show how a full rigorous semiclassical scheme for all orders of \hbar can be constructed for them without referring to the…
We consider a real periodic Schr\"odinger operator and a physically relevant family of $m \geq 1$ Bloch bands, separated by a gap from the rest of the spectrum, and we investigate the localization properties of the corresponding composite…
We present a computational approach which is tailored for reducing the complexity of the description of extended systems at the density functional theory level. We define a recipe for generating a set of localized basis functions which are…
The concept of Wannier-Stark ladders, describing the equally spaced spectrum of a tightly-bound particle in a constant electric field, is generalized to account for arbitrary slowly-varying potentials. It is shown that an abrupt transition…
An adaptation of the WKB method in the deformation quantization formalism is presented with the aim to obtain an approximate technique of solving the eigenvalue problem for energy in the phase space quantum approach. A relationship between…
Hybrid functionals often improve considerably the accuracy of density-functional calculations, in particular of quantities resulting from the band structure. In plane-wave (PW) calculations this benefit comes at the cost of an increase in…
In this paper, we consider the quantum-mechanical phase space patterns on ordered and disordered networks. For ordered networks in which each node is connected to its 2m nearest neighbors (m on either side), the phase space…
A general method is presented to unfold band structures of first-principles super-cell calculations with proper spectral weight, allowing easier visualization of the electronic structure and the degree of broken translational symmetry. The…
Construction of hybrid atomic orbitals is proposed as the approximate common eigen states of finite first moment matrices. Their hybridization and orientation can be a-priori tunned as per their anticipated neighbourhood. Their Wannier…