Related papers: Differential Form Valued Forms and Distributional …
We discuss the one-dimensional, general quadratic Hamiltonian and the bi-dimensional charged particle in time-dependent electromagnetic fields through the Lie algebraic approach. Such method consists in finding a set of generators that form…
This work outlines a time-domain numerical integration technique for linear hyperbolic partial differential equations sourced by distributions (Dirac $\delta$-functions and their derivatives). Such problems arise when studying binary black…
Evaluation of the angular distribution function of particles scattered in an amorphous medium is improved by deforming the integration path in the Fourier integral representation into the complex plane. That allows us to present the…
The tensor product of two differential forms of degree $p$ and $q$ is a multilinear form that is alternating in its first $p$ arguments and alternating in its last $q$ arguments. These forms, which are known as double forms or…
We address in this work the question of the discretization of two-dimensional periodic Dirac Hamiltonians. Standard finite differences methods on rectangular grids are plagued with the so-called Fermion doubling problem, which creates…
We consider the domain dependence of the best constant in the subcritical fractional Sobolev constant, $$ \lambda_{s,p}(\Omega):=\inf \left\{ [u]_{H^s(\mathbb{R}^N)}^2,\,\, u\in C^\infty_c(\Omega),\,\, \|u\|_{L^p(\Omega)}=1 \right\}, $$…
We consider a theory of a two-component Dirac fermion localized on a (2+1) dimensional brane coupled to a (3+1) dimensional bulk. Using the fermionic particle-vortex duality, we show that the theory has a strong-weak duality that maps the…
Jia and Dutra (J. Phys. A: Math. Gen. 39 (2006) 11877) have considered the one-dimensional non-Hermitian complexified potentials with real spectra in the context of position-dependent mass in Dirac equation. In their second example, a…
We consider the two Higgs doublet model extension of the Standard Model in the limit where all physical scalar particles are very heavy; too heavy, in fact, to be experimentally produced in forthcoming experiments. The symmetry breaking…
In these lectures we give, first, the model-independent analysis of the exclusive rare decays B -> K l(bar) l and B_c -> D(D*) l(bar) l with special emphasis on the cascade decay B_c -> D(*)(-> D pi) l(bar) l. We derive a four-fold angular…
We examine the properties of linear electrostatic waves in unmagnetized quantum and classical plasmas consisting of one or two populations of electrons with analytically tractable distribution functions in the presence of a stationary…
In this article we describe applications of Discrete Differential Forms in computational GR. In particular we consider the initial value problem in vacuum space-times that are spherically symmetric. The motivation to investigate this method…
In this paper the distribution of charged particles is constructed under the approximation of ambipolar diffusion. The results of mathematical modelling in two-dimensional case taking into account the velocities of the system are presented.
In this work, we investigate the quantum dynamics of a particle subject to the Morse potential within the framework of Dunkl quantum mechanics. By employing the Dunkl derivative operator, which introduces reflection symmetry, we construct a…
Given a domain G, a reflection vector field d(.) on the boundary of G, and drift and dispersion coefficients b(.) and \sigma(.), let L be the usual second-order elliptic operator associated with b(.) and \sigma(.). Under suitable…
The main goal of this thesis is to show the crucial role that plays the symbol in analysing the spectrum the sequence of matrices resulting from PDE approximation and in designing a fast method to solve the associated linear problem. In the…
Electron fractionalization is intimately related to topology. In one-dimensional systems, fractionally charged states exist at domain walls between degenerate vacua. In two-dimensional systems, fractionalization exists in quantum Hall…
We study perturbed Dirac operators of the form $ D_s= D + s\A :\Gamma(E^0)\rightarrow \Gamma(E^1)$ over a compact Riemannian manifold $(X, g)$ with symbol $c$ and special bundle maps $\A : E^0\rightarrow E^1$ for $s>>0$. Under a simple…
In multi-phase fluid flow, fluid-structure interaction, and other applications, partial differential equations (PDEs) often arise with discontinuous coefficients and singular sources (e.g., Dirac delta functions). These complexities arise…
Given an affine Poisson algebra, that is singular one may ask whether there is an associated symplectic form. In the smooth case the answer is obvious: for the symplectic form to exist the Poisson tensor has to be invertible. In the…