Position-dependent mass fractal Schrodinger equation from fractal anisotropy and product-like fractal measure and its implications in quantum dots and nanocrystals

El-Nabulsi, Rami Ahmad

doi:10.1007/s11082-021-03093-6

Cited by 33 publications

(2 citation statements)

References 91 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…For notable recent literature in the field, we refer to. [12][13][14][15][16][17][18][19][20][21][22][23][24] The PDM opens a new possibility, which is going to be explored in this paper. In particular, we are going to show how, using PDM, particles can be coupled through the kinetic part of the Hamiltonian.…”

Section: Introductionmentioning

confidence: 99%

A Non‐Standard Coupling Between Quantum Systems Originated From Their Kinetic Energy

Shushi

2023

Annalen der Physik

View full text Add to dashboard Cite

In standard quantum mechanics, the coupling between quantum systems is described by a potential interaction term in the Hamiltonian. This type of coupling is well‐rooted in nature and shapes the universe around us, from the interactions between single photons to the attractive force between atoms that forms molecules. Quantum mechanics does not forbid other kinds of interactions to take place. In this paper, a non‐standard quantum coupling between quantum systems is proposed, originated from the kinetic energy rather than the potential interaction in the Hamiltonian. Unlike the potential‐based coupling, the proposed coupling changes the fundamental structure of quantum mechanics in the form of modified uncertainty relations that are shaped by the coupling between the particles in the system. Two prototypical examples of non‐standard systems that perform such kinetic‐based coupling are presented. In the first example, it considers a particle confined in a heterostructure, such as a quantum dot, where the coupling is between the particle and dynamic walls that determine the size of the heterostructure. The second example involves a particle in a 3D heterostructure with coupling between its position axes. It then discusses several future implications of the proposed type of non‐standard coupling.

show abstract

Section: Introductionmentioning

confidence: 99%

A Non‐Standard Coupling Between Quantum Systems Originated From Their Kinetic Energy

Shushi

2023

Annalen der Physik

View full text Add to dashboard Cite

show abstract

“…In fact, this new concept was introduced recently by Li and Ostoja-Starzewski in order to describe dynamics in anisotropic and continuum media [42][43][44] and was motivated by Tarasov fractal calculus arguments [45,46]. It is considered a successful approach, which has proved to have several successful implications in sciences and engineering at different scales [47][48][49][50][51][52][53][54][55][56][57][58]. In the Li and Ostoja-Starzewski approach (LOSA henceforth), the dynamic equations of motion hold mathematical forms involving integer-order integrals, whereas their local forms are expressed through partial differential equations with integerorder derivatives except that they contain coefficients involving fractal dimensions.…”

Section: Introductionmentioning

confidence: 99%

Emergence of lump-like solitonic waves in Heimburg–Jackson biomembranes and nerves fractal model

El-Nabulsi

2022

J. R. Soc. Interface.

View full text Add to dashboard Cite

The aim of this study is to extend the soliton propagation model in biomembranes and nerves constructed by Heimburg and Jackson for the case of fractal dimensions. Our analyses are based on the product-like fractal measure concept introduced by Li and Ostoja-Starzewski in their attempt to explore anisotropic fractal elastic media and electromagnetic fields. The mathematical model presented in the paper is formulated for only a part of a single nerve cell (an axon). The analytical and numerical envelop soliton of this equation are reported. The results obtained prove the emergence of lump-type solitonic waves in nerves and biomembranes. In particular, these waves decay algebraically to the background wave in space direction. This scenario is viewed as a particular class of rational localized waves which are solutions of the integrable Ishimori I equation and the (2 + 1) Kadomtsev–Petviashvili I equation. The effects of fractal dimensions are discussed and were found to be significant to some extents.

show abstract

Modeling of combustion and turbulent jet diffusion flames in fractal dimensions

El-Nabulsi

Anukool

2022

Continuum Mech. Thermodyn.

View full text Add to dashboard Cite

Position-dependent mass fractal Schrodinger equation from fractal anisotropy and product-like fractal measure and its implications in quantum dots and nanocrystals

Cited by 33 publications

References 91 publications

A Non‐Standard Coupling Between Quantum Systems Originated From Their Kinetic Energy

A Non‐Standard Coupling Between Quantum Systems Originated From Their Kinetic Energy

Emergence of lump-like solitonic waves in Heimburg–Jackson biomembranes and nerves fractal model

Modeling of combustion and turbulent jet diffusion flames in fractal dimensions

Contact Info

Product

Resources

About