Related papers: Differential technique for the covariant orbital a…
Tracing the modifications of molecules in surface chemical reactions benefits from the possibility to image their orbitals. While delocalized frontier orbitals with {\pi}-character are imaged routinely with photoemission orbital tomography,…
Several algebro-geometric properties of commutative rings of partial differential operators as well as several geometric constructions are investigated. In particular, we show how to associate a geometric data by a commutative ring of…
We propose an efficient quantum algorithm for simulating the dynamics of general Hamiltonian systems. Our technique is based on a power series expansion of the time-evolution operator in its off-diagonal terms. The expansion decouples the…
The derivation of spherical harmonics is the same in nearly every quantum mechanics textbook and classroom. It is found to be difficult to follow, hard to understand, and challenging to reproduce by most students. In this work, we show how…
The transformation of radiation signals (e.g., photon occupation number and integrated intensity) between moving frames is a common task is physics, astrophysics and cosmology. Here we show that the required boost operator, relating the…
Orientational expansions, which are widely used in the natural sciences, exist in angular and Cartesian form. Although these expansions are orderwise equivalent, it is difficult to relate them in practice. In this article, both types of…
We analyze the two-orbital Hubbard model by means of the Composite Operator Method with the aim at studying the phenomenon of orbital selective Mott transition (OSMT). The model contains an interorbital interaction $U'$, in addition to the…
Using simultaneously two operator identities, we consider the inversion of the convolution operators on a rectangular. The structure of the inverse operators and of some corresponding forms, which are important in signal processing, is…
Dirac-Coulomb type differential equation and its solution relativistic exponential-type spinor orbitals are introduced. They provide a revised form for operator invariants, namely Dirac invariants, simplifying the treatment of the angular…
Parton distribution functions (PDFs) and light-cone distribution amplitudes (LCDAs) are central non-perturbative objects of interest in high-energy inelastic and elastic scattering, respectively. As a result, an ab-initio determination of…
Recently the partial wave cutoff method was developed as a new calculational scheme for a functional determinant of quantum field theory in radial backgrounds. For the contribution given by an infinite sum of large partial waves, we derive…
Previous studies on orbital angular momentum (OAM) communication mainly considered line-of-sight environments. In this letter, however, it is found that OAM communication with high-order modulation can be achieved in highly reverberant…
We investigate the dynamical properties of a type-II optical parametric oscillator pumped by a structured light beam carrying orbital angular momentum. Different dynamical regimes are theoretically derived and experimentally demonstrated,…
We present a novel technique for generating beams of light carrying orbital angular momentum (OAM) that increases mode purity and decreases singularity splitting by orders of magnitude. This technique also works to control and mitigate beam…
We propose a method for sorting electrons by orbital angular momentum (OAM). Several methods now exist to prepare electron wavefunctions in OAM states, but no technique has been developed for efficient, parallel measurement of pure and…
A convolutional neural network is used to align an orbital angular momentum sorter in a transmission electron microscope. The method is demonstrated using simulations and experimentally. As a result of its accuracy and speed, it offers the…
We review the quadratic form of the Laplace operator in 3 dimensions in spehrical coordinates which acts on the transverse components of vector functions. Operators, acting on the parametrizing functions of one of the transverse components…
We address the problem of angular momentum decomposition of a free photon. We propose a natural and physical scheme for separating the total angular momentum operator for a free photon into an orbital part and a spin part with the hope that…
Accurately forecasting the long-term evolution of turbulence represents a grand challenge in scientific computing and is crucial for applications ranging from climate modeling to aerospace engineering. Existing deep learning methods,…
We use the theory of functions of noncommuting operators (noncommutative analysis) to solve an asymptotic problem for a partial differential equation and show how, starting from general constructions and operator formulas that seem to be…