Related papers: An envelope function formalism for lattice-matched…
This paper presents a renormalization approach to many-particle systems. By starting from a bare Hamiltonian ${\cal H}= {\cal H}_0 +{\cal H}_1$ with an unperturbed part ${\cal H}_0$ and a perturbation ${\cal H}_1$,we define an effective…
A strategy for the systematic design of polymeric superlattices with tailor-made mini-bandgaps and carrier mini-effective masses is described and computationally implemented by means of an envelope crystalline-orbital method, which is a…
The envelope theory, also known as the auxiliary field method, is a simple technique to compute approximate solutions of Hamiltonians for $N$ identical particles in $D$ dimensions. The quality of the approximate eigenvalues can be improved…
A spectrally formulated finite element analysis based methodology has been proposed to calculate phononic band structure of reticulated honeycomb lattices having translationally invariant repetitive elements called unit cells. Bloch…
Electronic structure codes usually allow to calculate the work function as a part of the theoretical description of surfaces and processes such as adsorption thereon. This requires a proper calculation of the electrostatic potential in all…
We present a new method for calculating electronic states in low-dimensional semiconductor heterostructures, which is based on the real-space Hamiltonian in the envelope function approximation. The numerical implementation of the method is…
We demonstrate that all of the salient features of the Harper-Hofstadter model can be implemented with ultracold atoms trapped in a bichromatic ring-shaped lattice. Using realistic sinusoidal lattice potentials rather than assume the…
The modelling of heterogeneous and architected materials poses a significant challenge, demanding advanced homogenisation techniques. However, the complexity of this task can be considerably simplified through the application of micropolar…
We present an approach to solid-state electronic-structure calculations based on the finite-element method. In this method, the basis functions are strictly local, piecewise polynomials. Because the basis is composed of polynomials, the…
We propose a system-oriented basis-set design based on even-tempered basis functions to variationally encode electronic ground-state information into molecular orbitals. First, we introduce a reduced formalism of concentric even-tempered…
Even small electrostatic potentials can dramatically influence the band structure of narrow-, broken-, and inverted-gap materials. A quantitative understanding often necessitates a self-consistent Hartree approach. The valence and…
Spin-orbit beams, in which the orbital angular momentum degree of freedom is coupled to a two-level system such as polarization of light or spin in electrons and neutrons, have gained significant interest for their unique propagation…
It is shown that the parameters contained in any two complete solutions of the Hamilton-Jacobi equation, corresponding to a given Hamiltonian, are related by means of a time-independent canonical transformation and that, in some cases, a…
In this work we propose an efficient and accurate multi-scale optical simulation algorithm by applying a numerical version of slowly varying envelope approximation in FEM. Specifically, we employ the fast iterative method to quickly compute…
Lattice models are popular methods for simulating deformation of solids by discretizing continuum structures into spring networks. Despite the simplicity and efficiency, most lattice models only rigorously converge to continuum models for…
A monolithic coupling between the material point method (MPM) and the finite element method (FEM) is presented. The MPM formulation described is implicit, and the exchange of information between particles and background grid is minimized.…
Closed-form expressions for all matrix elements required for variational calculation of the electronic structure of periodic solids have been derived using a basis of explicitly correlated Gaussians (ECGs). Periodic basis functions are…
The envelope theory is a method to easily obtain approximate, but reliable, solutions for some quantum many-body problems. Quite general Hamiltonians can be considered for systems composed of an arbitrary number of different particles in…
In this work we describe a new technique for numerical exact diagonalization. The method is particularly suitable for cold bosonic atoms in optical lattices, in which multiple atoms can occupy a lattice site. We describe the use of the…
Whether a system is to be considered complex or not depends on how one searches for correlations. We propose a general scheme for calculation of entropies in lattice systems that has high flexibility in how correlations are successively…