Related papers: Capacitance and charging of metallic objects
It is shown that the operator methods of supersymmetric quantum mechanics and the concept of shape invariance can profitably be used to derive properties of spherical harmonics in a simple way. The same operator techniques can also be…
We apply Colombeau-type regularization to the electromagnetic field of a point-charge and show how the Li\'{e}nard-Wiechert potential can be derived from a generalized function based on the geometry of Minkowski space. Furthermore, for a…
In the recent experiments [Chmiola et al, Science 313, 1760 (2006); Largeot et al, J. Am. Chem. Soc. 130, 2730 (2008)] an anomalous increase of the capacitance with a decrease of the pore size of a carbon-based porous electric double-layer…
For an arbitrary electromagnetic field, we define a prepotential $S$, which is a complex-valued function of spacetime. The prepotential is a modification of the two scalar potential functions introduced by E. T. Whittaker. The prepotential…
We discuss the electromagnetic properties of both a charged free particle, and a charged particle bounded by an harmonic potential, within collapse models. By choosing a particularly simple, yet physically relevant, collapse model, and…
A broadband electromagnetic source is important for scientific and technological applications. Quantum vacuum fluctuations, which manifest most prominently in the Casimir effect, provide a fundamentally broadband electromagnetic source.…
We represent a matrix representation of the Neumann-Poincar\'e operator defined on the boundaries of a torus. A torus is a doubly connected domain in three dimensions. There is a well-known parametrization for the shape of the torus, the…
The quantum mechanical expression relating two commuting operators is reformulated such that the power method (also called method of moments) for iteratively calculating eigenvalues and eigenvectors becomes applicable. The new iterative…
We consider the problem of estimating the eigenvalues and the integral of the corresponding eigenfunctions, associated to the Newtonian potential operator, defined in a bounded domain $\Omega \subset \mathbb{R}^{d},$ where $d = 2, 3$, in…
The Boltzmann distribution of electrons poses a fundamental barrier to lowering energy dissipation in conventional electronics, often termed as Boltzmann Tyranny. Negative capacitance in ferroelectric materials, which stems from the stored…
A meta-surface made of a collection of nano-resonators characterized an electric dipole and a magnetic dipole was studied in the regime where the wavelength is large with respect to the size of the resonators. An effective description in…
Unlike conventional two-dimensional (2D) semiconductor superlattices, moir\'{e} patterns in 2D materials are flexible and their electronic, magnetic, optical, and mechanical properties depend on their topography. Within a…
In this paper we prove that solutions to several shape optimization problems in the plane, with a convexity constraint on the admissible domains, are polygons. The main terms of the shape functionals we consider are either E f ($\Omega$),…
High-precision knowledge of electromagnetic form factors of nuclei is a subject of much current experimental and theoretical activity in nuclear and atomic physics. Such precision mandates that effects of the non-zero spatial extent of the…
MXene, the class of two-dimensional materials, has been found to be useful as potential electrode materials for electrochemical capacitors. Although experimental investigation on the electrochemical performances of a few MXenes have been…
We show how to describe the coupling of electrons to non-uniform magnetic fields in the framework of the widely used norm-conserving pseudopotential appro ximation for electronic structure calculations. Our derivation applies to magnetic…
The integrability condition called shape invariance is shown to have an underlying algebraic structure and the associated Lie algebras are identified. These shape-invariance algebras transform the parameters of the potentials such as…
An approximate analytical expression for "capacitance" of MWPC configurations circulates in the literature since decades and is copied over and over again. In this paper we will try to show that this formula corresponds to a physical…
In this paper we investigate the shape invariance property of a potential in one dimension. We show that a simple ansatz allows us to reconstruct all the known shape invariant potentials in one dimension. This ansatz can be easily extended…
The properties of nuclear matter are studied using state-of-the-art nucleon-nucleon forces up to fifth order in chiral effective field theory. The equations of state of symmetric nuclear matter and pure neutron matter are calculated in the…