Related papers: Dirac lattices, zero-range potentials and self adj…
Describing long-ranged electrostatics using short-ranged pair potentials is appealing since the computational complexity scales linearly with the number of particles. The foundation of this approach is to mimic the long-ranged medium…
We present new aspects of the electromagnetic field by introducting the natural potentials. These natural potentials are suitable for constructing the first order distortions of the metric tensor of Complex Relativity - the theory combining…
In this paper we derive an expression for the static electric polarizability of a particle bound by a finite potential well without the explicit use of the continuum states in our calculations. This will be accomplished by employing the…
In the present paper, we solve the Dirac equation in the 2+1 dimensional exponentially expanding magnetized by uniform magnetic field and non-magnetized universes, separately. Asymptotic behaviors of the solutions are determined. Using…
Under certain reality conditions, a general solution to the dispersionless Toda lattice hierarchy describes deformations of simply-connected plane domains with a smooth boundary. The solution depends on an arbitrary (real positive) function…
Maxwell's equations resemble Schr\"odinger's equation in that an exact solution for a well-defined model delivers all physically relevant details. Solvable microscopic electrodynamic models, however, are rare. An exception is the discrete…
Fundamental properties of spontaneous and piezo polarization are reformulated and critically reviewed. It was demonstrated that Landau definition of polarization as a dipole density could be used to the infinite systems. The difference…
In applying large-momentum effective theory, renormalization of the Euclidean correlators in lattice regularization is a challenge due to linear divergences in the self-energy of Wilson lines. Based on lattice QCD matrix elements of the…
We use two renormalization techniques, Effective Field Theory and the Similarity Renormalization Group, to solve simple Schr{\"o}dinger equations with delta-function potentials in one and two dimensions. The familiar one-dimensional…
We obtain exact solutions to the two-dimensional (2D) Dirac equation for the one-dimensional P\"oschl-Teller potential which contains an asymmetry term. The eigenfunctions are expressed in terms of Heun confluent functions, while the…
Two-dimensional (2D) electronic materials are of significant technological interest due to their exceptional properties and broad applicability in engineering. The transition from nanoscale physics, that dictates their stable…
Metasurfaces are a powerful tool for manipulating light using small structures on the nanoscale. In most meta-surfaces, near-field couplings are treated as unfavorable perturbations. Here, we experimentally investigate a structure…
This article offers a new approach for analysing the dynamic behaviour of distributions of charged particles in an electromagnetic field. After discussing the limitations inherent in the Lorentz-Dirac equation for a single point particle a…
We report the polarization-dependent electromagnetic response from a series of novel terahertz (THz) metasurfaces where asymmetry is introduced through the displacement of two adjacent metallic arms separated by a distance $\delta$. For all…
The dipole-multipole transition in rapidly rotating dynamos is investigated through the analysis of forced magnetohydrodynamic waves in an unstably stratified fluid. The focus of this study is on the inertia-free limit applicable to…
A flexoelectric peridynamic (PD) theory is proposed. Using the PD framework, the formulation introduces, perhaps for the first time, a nanoscale flexoelectric coupling that entails non-uniform strain in centrosymmetric dielectrics. This…
We employ density functional theory to study in detail the crystallization of super-paramagnetic particles in two dimensions under the influence of an external magnetic field that lies perpendicular to the confining plane. The field induces…
We consider several mathematical issues regarding models that simulate forces exerted by cells. Since the size of cells is much smaller than the size of the domain of computation, one often considers point forces, modelled by Dirac Delta…
A new general formalism for determining the electric multipole polarizabilities of quantum (atomic and nuclear) bound systems based on the use of the transition matrix in momentum space has been developed. As distinct from the conventional…
Dipole condensates, formed from particle-hole pairs, represent a unique class of charge-neutral quantum fluids that evade conventional vector gauge fields, making their electrodynamic responses difficult to probe in natural materials. Here,…