Mapping Between Charge-Dyon and Position-Dependent Mass Systems*

Abstract

The primary purpose of this work is to reproduce the scenario composed of a charge-dyon system utilizing position-dependent effective mass (PDM) background in the non-relativistic and in the relativistic regimes. In the non-relativistic case we substitute the exact charge-dyon eigenfunction into PDM Schrödinger equation, in the Zhu-Kroemer parametrization, and then solve it for the mass distribution considering M = M(r). Analogously, in the relativistic case we study the Klein-Gordon equation for a position-dependent mass, and in this case, we are able to analytically solve the equation for M = M(r,θ).

The conjugate gradient approach to solve two dimensions linear elliptic boundary value equations as a prototype of the reaction diffusion system

“…Scilab is an open-source alternative to MATLAB [13]. It places less emphasis on syntactic compatibility with MATLAB; however, it is sufficiently comparable for some authors to assert that it is simple to transfer skills between them [14].…”

“…In quantitatively oriented scientific subjects such as engineering and physics, partial different ial equations are prevalent. These concepts, such as the Schrödinger equation and the Pauli equation, play a crucial role in the development of modern scientific understanding in several fields including sound, heat, diffusion, electrostatics, electrodynamics, thermodynamics, fluid dynamics, elasticity, general relativity, and quantum mechanics [8][9][10][11][12][13]. Additionally, these concepts arise from a range of mathematical concerns, including differential geometry and the calculus of variations.…”

Introdução à Física do Monopolo Magnético: uma abordagem clássica

“…Isto é, recuperamos a solução radial 14 (11). Este resultado indica não ser possível verificar a constância do módulo de v partindo diretamente das expressões ( 47) ou (49), pois pelo resultado visto em (57), teríamos que primeiro isolar v 2 na solução radial (11), o que cairia numa expressão envolvendo o próprio r 2 , resultando numa identidade com a derivada temporal de v em ambos os lados da igualdade. Para demonstrarmos a constância do módulo de v, seguiremos por outro caminho.…”

“…Autores/ano Carga-monopolo Schmidt, Jesus/2018 [48] Carga-dyon Jesus, Schmidt/2019 [49] Carga-monopolo relativístico Jesus, Schmidt/2019 [49] Carga-monopolo com spin-1/2 Jesus, Schmidt/2019 [50] informações a respeito de seu comportamento, inúmeros modelos análogos teóricos e experimentais (tanto clássicos como quânticos) podem ser obtidos.…”

Mapping between conical space and non-relativistic position-dependent effective mass systems

“…Recently the authors proposed a methodology to map a PDM quantum system-in principle it could be built in laboratory-into a given quantum system which at present cannot be experimentally realized. We presented two examples: the Dirac magnetic monopole [19] and the dyon [20]. The idea of simulating such kind of systems-either because it is unrealizable, see for instance [21], or because it is quite difficult to reproduce-using a controllable condensed matter system was explored in several previous works [22][23][24] using optical techniques.…”