Related papers: Dimensional Analysis and electric potential due to…
When one slightly pushes a thin elastic sheet at its center into a hollow cylinder, the sheet forms (to a high degree of approximation) a developable cone, or "d-cone" for short. Here we investigate one particular aspect of d-cones, namely…
We develop an analytical procedure to compute all relevant physical properties of scalar field oscillons in models with quartic polynomial potentials: energy, radius, frequency, core-amplitude, and lifetime. We compare our predictions to…
The electrostatics properties of composite materials with fractal geometry are studied in the framework of fractional calculus. An electric field in a composite dielectric with a fractal charge distribution is obtained in the spherical…
In this article we discuss a procedure to solve the one dimensional (1D) Schroedinger Equation for a periodic potential, which may be well suited to teach band structure theory. The procedure is conceptually very simple, so that it may be…
We study the electronic energy spectra and wave functions on the square Fibonacci tiling, using an off-diagonal tight-binding model, in order to determine the exact nature of the transitions between different spectral behaviors, as well as…
In one dimension one can dissect a scattering potential $ v(x) $ into pieces $ v_i(x) $ and use the notion of the transfer matrix to determine the scattering content of $ v(x) $ from that of $ v_i(x) $. This observation has numerous…
A new repeated-slab calculation method is developed to simulate the electronic structures of charged surfaces by arranging density-variable charged sheets in vacuum regions to realize a constant potential on the charged sheets and maintain…
We relax the usual diagonal constraint on the matrix representation of the eigenvalue wave equation by allowing it to be tridiagonal. This results in a larger solution space that incorporates an exact analytic solution for the non-central…
The supersymmetric quantum mechanics of a two-dimensional non-relativistic particle subject to external magnetic and electric fields is studied in a superfield formulation and with the typical non-minimal coupling of (2+1) dimensions. Both…
In the framework of Clifford analysis, a chain of harmonic and monogenic potentials in the upper half of Euclidean space R^{m+1} was constructed recently, including a higher dimensional analogue of the logarithmic function in the complex…
The electrostatics problem of a point charge next to a conducting plane is best solved by placing an image charge placed on the opposite side. For a charge between two parallel planes this can be solved with image charges outside the planes…
We study the potential and the charge distribution across the interface of a plasma and a dielectric wall. For this purpose, the charge bound to the wall is modelled as a quasi-stationary electron surface layer which satisfies Poisson's…
For several configurations of charges in the presence of conductors, the method of images permits us to obtain some observables associated with such a configuration by replacing the conductors with some image charges. However, simple…
We extend density matrix embedding theory to periodic systems, resulting in an electronic band structure method for solid-state materials. The electron correlation can be captured by means of a local impurity model using various choices of…
An exponential interaction is constructed so that one-dimensional atoms and chains of atoms mimic the general behavior of their three-dimensional counterparts. Relative to the more commonly used soft-Coulomb interaction, the exponential…
An interesting fundamental problem in density-functional theory of electronic structure of matter is to construct the exact Kohn-Sham (KS) potential for a given density. The exact potential can then be used to assess the accuracy of…
We present a theory to compute the force due to light upon a particle on a dielectric plane by the Coupled Dipole Method (CDM). We show that, with this procedure, two equivalent ways of analysis are possible, both based on Maxwell's stress…
In electronic structure calculations, the correlation energy is defined as the difference between the mean field and the exact solution of the non relativistic Schr\"odinger equation. Such an error in the different calculations is not…
In this paper, the approach for considering fast charged particles scattering on targets of complex structure, which contains some isolated substructures, was expanded to account quadratic potential terms. Based on this approach, the…
We investigate generalized potentials for a mean-field density functional theory of a three-phase contact line. Compared to the symmetrical potential introduced in our previous article [1], the three minima of these potentials form a small…