Discussion on Exact Solution of Dirac Equation with Generalized Exponential Potential in the Presence of Generalized Uncertainty Principle

2021 ◽  
Vol 62 (3) ◽  
Author(s):  
Zi-Long Zhao ◽  
Hao Wu ◽  
Zheng-Wen Long
Keyword(s):  
Exact Solution ◽  
Dirac Equation ◽  
Uncertainty Principle ◽  
Generalized Uncertainty Principle ◽  
Exponential Potential

scholarly journals Exotic fermionic fields and minimal length

2020 ◽  
Vol 80 (8) ◽  
Author(s):  
J. M. Hoff da Silva ◽  
D. Beghetto ◽  
R. T. Cavalcanti ◽  
R. da Rocha
Keyword(s):  
Dirac Equation ◽  
Quantum Gravity ◽  
Dirac Operator ◽  
Uncertainty Principle ◽  
Generalized Uncertainty Principle ◽  
Minimal Length ◽  
Dynamical Equations ◽  
Spacetime Manifold ◽  
Fermionic Fields

Abstract We investigate the effective Dirac equation, corrected by merging two scenarios that are expected to emerge towards the quantum gravity scale. Namely, the existence of a minimal length, implemented by the generalized uncertainty principle, and exotic spinors, associated with any non-trivial topology equipping the spacetime manifold. We show that the free fermionic dynamical equations, within the context of a minimal length, just allow for trivial solutions, a feature that is not shared by dynamical equations for exotic spinors. In fact, in this coalescing setup, the exoticity is shown to prevent the Dirac operator to be injective, allowing the existence of non-trivial solutions.

Perturbative calculation of energy levels for the Dirac equation with generalized momenta

2020 ◽  
Vol 35 (20) ◽  
pp. 2050106
Author(s):  
Marco Maceda ◽  
Jairo Villafuerte-Lara
Keyword(s):  
Dirac Equation ◽  
Uncertainty Principle ◽  
Energy Levels ◽  
Generalized Uncertainty Principle ◽  
Spatial Dimension ◽  
Three Dimensions ◽  
Minimum Length ◽  
Linear Potential ◽  
Perturbative Calculation ◽  
Square Well

We analyze a modified Dirac equation based on a noncommutative structure in phase space originating from a generalized uncertainty principle with a minimum length. The noncommutative structure induces generalized momenta and contributions to the energy levels of the standard Dirac equation. Applying techniques of perturbation theory, we find the lowest-order corrections to the energy levels and eigenfunctions of the Dirac equation in three dimensions for a spherically symmetric linear potential and for a square-well times triangular potential along one spatial dimension. We find that the corrections due to the noncommutative contributions may be of the same order as the relativistic ones, leading to an upper bound on the parameter fixing the minimum length induced by the generalized uncertainty principle.

scholarly journals Dynamics of quintessence in generalized uncertainty principle

2020 ◽  
Vol 80 (10) ◽  
Author(s):  
Alex Giacomini ◽  
Genly Leon ◽  
Andronikos Paliathanasis ◽  
Supriya Pan
Keyword(s):  
Uncertainty Principle ◽  
Critical Points ◽  
System Analysis ◽  
Field Model ◽  
Generalized Uncertainty Principle ◽  
De Sitter ◽  
Exponential Potential ◽  
Isotropic Universe ◽  
General Potential ◽  
Quintessence Model

AbstractWe investigate the quintessence scalar field model modified by the generalized uncertainty principle in the background of a spatially flat homogeneous and isotropic universe. By performing a dynamical system analysis we examine the nature of the critical points and their stability for two potentials, one is the exponential potential and the other is a general potential. In the case of an exponential potential, we find some new critical points for this modified quintessence scenario that describe the de Sitter universes, and these critical points do not appear in the standard quintessence model with an exponential potential. This is one of the main results of this work. Now for the general potential our analysis shows that the physical properties of the critical points remain exactly the same as for the exponential potential which means that within this modified quintessence scenario all kind of potentials have same behaviour. This kind of result is completely new in cosmology because with the change of the potential, differences are usually expected in all respect.

Solution of the Dirac equation with exponential-type potential under the GUP

2021 ◽  
Vol 36 (01) ◽  
pp. 2150005
Author(s):  
Lin-Fang Deng ◽  
He-Yao Zhang ◽  
Chao-Yun Long
Keyword(s):  
Dirac Equation ◽  
Uncertainty Principle ◽  
Exponential Type ◽  
Generalized Uncertainty Principle ◽  
Pseudospin Symmetry ◽  
Heisenberg Uncertainty Principle ◽  
Heisenberg Uncertainty ◽  
Uvarov Method ◽  
Planck Energy ◽  
Type Potential

In quantum gravity theories, when the scattering energy is comparable to the Planck energy, the usual Heisenberg uncertainty principle breaks down and is replaced by generalized uncertainty principle (GUP). In this paper, the Dirac equation is studied for a single particle with spin and pseudospin symmetry in the presence of GUP, in [Formula: see text] dimensions. For arbitrary wave [Formula: see text], the Dirac equation with multiparameter exponential-type potential is solved by applying the approximation of the centrifugal term and the Nikiforov–Uvarov method. The corresponding energy spectra and eigenvalue function are obtained in the closed form and depend on the GUP parameter. In addition, several interesting cases have been discussed.

Scattering state in GUP by Milne’s differential equation

2018 ◽  
Vol 33 (39) ◽  
pp. 1850231 ◽  
Author(s):  
A. Armat ◽  
S. Mohammad Moosavi Nejad
Keyword(s):  
Differential Equation ◽  
Dirac Equation ◽  
Nonlinear Differential Equation ◽  
Uncertainty Principle ◽  
Generalized Uncertainty Principle ◽  
Minimal Length ◽  
Nuclear Potential ◽  
Saxon Potential ◽  
One Dimensional ◽  
Scattering State

In this paper, our main aim is to obtain the transmission (T) and the reflection (R) coefficients for one-dimensional scattering state of the spin-[Formula: see text] particles in an interaction with a special nuclear potential. For this reason, at first, we consider Dirac equation and then obtain the Milne’s nonlinear differential equation due to minimal length from Schrödinger-like equation and then calculate the T- and R-coefficients using one-dimensional Woods–Saxon potential on the basis of the generalized uncertainty principle. Finally, we will check the validity and the correctness of our results.

Quantum gravity corrections to tunneling of spin-1/2 fermions from Kerr–Newman Black Hole

2021 ◽  
pp. 2150123
Author(s):  
Aheibam Keshwarjit Singh ◽  
Irom Ablu Meitei ◽  
Telem Ibungochouba Singh ◽  
Kangujam Yugindro Singh
Keyword(s):  
Black Hole ◽  
Electromagnetic Field ◽  
Dirac Equation ◽  
Quantum Gravity ◽  
Uncertainty Principle ◽  
Generalized Uncertainty Principle ◽  
Hawking Temperature ◽  
Curved Space ◽  
Gravity Effects ◽  
Newman Black Hole

In this paper, we solve the Dirac Equation in curved space–time, modified by the generalized uncertainty principle, in the presence of an electromagnetic field. Using this, we study the tunneling of [Formula: see text]-spin fermions from Kerr–Newman black hole. Corrections to the Hawking temperature and entropy of the black hole due to quantum gravity effects are also discussed.

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