Related papers: Understanding excitons using spherical geometry
We consider the quantum ferromagnetic Heisenberg model in three dimensions, for all spins $S\geq 1/2$. We rigorously prove the validity of the spin-wave approximation for the excitation spectrum, at the level of the first non-trivial…
The binding energy and the corresponding wave function of excitons in GaAs-based finite square quantum wells (QWs) are calculated by the direct numerical solution of the three-dimensional Schroedinger equation. The precise results for the…
A new gridding technique for the solution of partial differential equations in cubical geometry is presented. The method is based on volume penalization, allowing for the imposition of a cubical geometry inside of its circumscribing sphere.…
We study large traveling surface waves within a two-dimensional finite depth, free boundary, homogeneous, incompressible and viscous fluid governed by Darcy's law. The fluid is bound by a gravitational force to a flat rigid bottom and meets…
We present a computational approach for exciton calculations in two-dimensional (2D) materials within the Bethe-Salpeter equation (BSE) framework, employing an atomistic description with point-like orbitals. Unlike widespread efficient…
We formulated an effective theory for a single interlayer exciton in a bilayer quantum antiferromagnet, in the limit that the holon and doublon are strongly bound onto one interlayer rung by the Coulomb force. Upon using a rung linear spin…
We summarise the construction of exact axisymmetric scale-discretised wavelets on the sphere and on the ball. The wavelet transform on the ball relies on a novel 3D harmonic transform called the Fourier-Laguerre transform which combines the…
We consider the propagation of linear gravity waves on the free surface of steady, axisymmetric flows with purely azimuthal velocity. We propose a two-dimensional set of governing equations for surface waves valid in the deep-water limit.…
We develop a new higher order closed-form model for the dynamics of a hyperelastic isotropic 3D cylindrical body. We derive, for the first time, a simple explicit expression for the fundamental frequency.
A high-performance shooting algorithm is developed to compute time-periodic solutions of the free-surface Euler equations with spectral accuracy in double and quadruple precision. The method is used to study resonance and its effect on…
This paper presents a numerical compression strategy for the boundary integral equation of acoustic scattering in two dimensions. These equations have oscillatory kernels that we represent in a basis of wave atoms, and compress by…
The energy spectra and wavefunctions of bound excitons in important two-dimensional (2D) graphene derivatives, i.e., graphyne and graphane, are found to be strongly modified by quantum confinement, making them qualitatively different from…
The existence of strongly bound excitons is one of the hallmarks of the newly discovered atomically thin semi-conductors. While it is understood that the large binding energy is mainly due to the weak dielectric screening in two dimensions…
In this colloquium, we review the research on excitons in van der Waals heterostructures from the point of view of variational calculations. We first make a presentation of the current and past literature, followed by a discussion on the…
Excitons are bound states of electrons and holes whose band topology arises from an interplay between the topology of the underlying electronic bands and the structure of the electron-hole interaction. In crystalline solids, symmetry…
By an idealized quantum mechanical model, we formally describe the dispersion of nonretarded electromagnetic waves that express charge density oscillations near a fixed plane in three spatial dimensions (3D) at zero temperature. Our goal is…
We demonstrate the possibility of existence of indirect moving Wannier-Mott excitons in graphene. Electron-hole binding is conditioned by the trigonal warping of conic energy spectrum. The binding energies are found for the lowest exciton…
We study the particle-hole exciton mode in the QED3 theory of a phase-fluctuating d-wave superconductor in ladder approximation. We derive a Schroedinger-like equation for the exciton bound state and determine the conditions for its…
We provide accurate expressions for the $s$-wave scattering length for a Gaussian potential well in one, two and three spatial dimensions. The Gaussian potential is widely used as a pseudopotential in the theoretical description of…
A new formalism is derived for the analysis and exact reconstruction of band-limited signals on the sphere with directional wavelets. It represents an evolution of the wavelet formalism developed by Antoine & Vandergheynst (1999) and Wiaux…