scholarly journals ANALYTICAL SOLUTION OF (2+1) DIMENSIONAL DIRAC EQUATION IN TIME-DEPENDENT NONCOMMUTATIVE PHASE-SPACE

2020 ◽  
Vol 60 (2) ◽  
pp. 111-121
Author(s):  
Ilyas Haouam
Keyword(s):  
Phase Space ◽  
Dirac Equation ◽  
Analytical Solution ◽  
General Solution ◽  
Time Dependent ◽  
Noncommutative Phase Space ◽  
Invariant Method ◽  
Knowing That ◽  
Dirac Hamiltonian

In this article, we studied the system of a (2+1) dimensional Dirac equation in a time-dependent noncommutative phase-space. More specifically, we investigated the analytical solution of the corresponding system by the Lewis-Riesenfeld invariant method based on the construction of the Lewis-Riesenfeld invariant. Knowing that we obtained the time-dependent Dirac Hamiltonian of the problem in question from a time-dependent Bopp-Shift translation, then used it to set the Lewis- Riesenfeld invariant operators. Thereafter, the obtained results were used to express the eigenfunctions that lead to determining the general solution of the system.

scholarly journals ON THE THREE-DIMENSIONAL PAULI EQUATION IN NONCOMMUTATIVE PHASE-SPACE

2021 ◽  
Vol 61 (1) ◽  
pp. 230-241
Author(s):  
Ilyas Haouam
Keyword(s):  
Phase Space ◽  
Continuity Equation ◽  
Helmholtz Free Energy ◽  
Three Dimensional ◽  
Noncommutative Phase Space ◽  
Pauli Equation ◽  
Knowing That ◽  
The One ◽  
Magnetization Current ◽  
Space Noncommutativity

In this paper, we obtained the three-dimensional Pauli equation for a spin-1/2 particle in the presence of an electromagnetic field in a noncommutative phase-space as well as the corresponding deformed continuity equation, where the cases of a constant and non-constant magnetic fields are considered. Due to the absence of the current magnetization term in the deformed continuity equation as expected, we had to extract it from the noncommutative Pauli equation itself without modifying the continuity equation. It is shown that the non-constant magnetic field lifts the order of the noncommutativity parameter in both the Pauli equation and the corresponding continuity equation. However, we successfully examined the effect of the noncommutativity on the current density and the magnetization current. By using a classical treatment, we derived the semi-classical noncommutative partition function of the three-dimensional Pauli system of the one-particle and N-particle systems. Then, we employed it for calculating the corresponding Helmholtz free energy followed by the magnetization and the magnetic susceptibility of electrons in both commutative and noncommutative phase-spaces. Knowing that with both the three-dimensional Bopp-Shift transformation and the Moyal-Weyl product, we introduced the phase-space noncommutativity in the problems in question.

scholarly journals Solution of Dirac Equation with the Time-Dependent Linear Potential in Non-Commutative Phase Space

2013 ◽  
Vol 04 (07) ◽  
pp. 940-944 ◽  
Author(s):  
Xueling Jiang ◽  
Chaoyun Long ◽  
Shuijie Qin
Keyword(s):  
Phase Space ◽  
Dirac Equation ◽  
Time Dependent ◽  
Linear Potential

scholarly journals Deformation of the quintom cosmological model and its consequences

2018 ◽  
Vol 27 (03) ◽  
pp. 1850025 ◽  
Author(s):  
J. Sadeghi ◽  
B. Pourhassan ◽  
Z. Nekouee ◽  
M. Shokri
Keyword(s):  
Dark Energy ◽  
Phase Space ◽  
Cosmological Model ◽  
Cosmological Constant ◽  
Cosmological Parameters ◽  
Time Dependent ◽  
Noether Symmetry ◽  
Noncommutative Phase Space ◽  
Deformation Parameters ◽  
Noncommutative Parameter

In this paper, we investigate the effects of noncommutative phase-space on the quintom cosmological model. In that case, we discuss about some cosmological parameters and show that they depend on the deformation parameters. We find that the noncommutative parameter plays important role which helps to re-arrange the divergency of cosmological constant. We draw time-dependent scale factor and investigate the effect of noncommutative parameters. Finally, we take advantage from noncommutative phase-space and obtain the deformed Lagrangian for the quintom model. In order to discuss some cosmological phenomena as dark energy and inflation, we employ Noether symmetry.

scholarly journals Non-Hermitian Dirac Hamiltonian in Three-Dimensional Gravity and Pseudosupersymmetry

2015 ◽  
Vol 2015 ◽  
pp. 1-8 ◽  
Author(s):  
Özlem Yeşiltaş
Keyword(s):  
Dirac Equation ◽  
Three Dimensional ◽  
Space Time ◽  
Time Dependent ◽  
Quantum Mechanical ◽  
De Sitter ◽  
Metric Tensor ◽  
Curved Space ◽  
Dimensional Gravity ◽  
Dirac Hamiltonian

The Dirac Hamiltonian in the(2+1)-dimensional curved space-time has been studied with a metric for an expanding de Sitter space-time which is two spheres. The spectrum and the exact solutions of the time dependent non-Hermitian and angle dependent Hamiltonians are obtained in terms of the Jacobi and Romanovski polynomials. Hermitian equivalent of the Hamiltonian obtained from the Dirac equation is discussed in the frame of pseudo-Hermiticity. Furthermore, pseudosupersymmetric quantum mechanical techniques are expanded to a curved Dirac Hamiltonian and a partner curved Dirac Hamiltonian is generated. Usingη-pseudo-Hermiticity, the intertwining operator connecting the non-Hermitian Hamiltonians to the Hermitian counterparts is found. We have obtained a new metric tensor related to the new Hamiltonian.

scholarly journals On the (2 + 1)-dimensional Dirac equation in a constant magnetic field with a minimal length uncertainty

2015 ◽  
Vol 24 (02) ◽  
pp. 1550016 ◽  
Author(s):  
P. Pedram ◽  
M. Amirfakhrian ◽  
H. Shababi
Keyword(s):  
Magnetic Field ◽  
Wave Function ◽  
Dirac Equation ◽  
General Solution ◽  
Harmonic Oscillator ◽  
Constant Magnetic Field ◽  
Minimal Length ◽  
Two Dimensional ◽  
Quantum Numbers ◽  
Dirac Hamiltonian

In this paper, we exactly solve the (2 + 1)-dimensional Dirac equation in a constant magnetic field in the presence of a minimal length. Using a proper ansatz for the wave function, we transform the Dirac Hamiltonian into two two-dimensional nonrelativistic harmonic oscillator and obtain the solutions without directly solving the corresponding differential equations which are presented by Menculini et al. [Phys. Rev. D 87 (2013) 065017]. We also show that Menculini et al. solution is a subset of the general solution which is related to the even quantum numbers.

scholarly journals Berry Phase for Time-Dependent Coupled Harmonic Oscillators in the Noncommutative Phase Space via Path Integral Techniques

2020 ◽  
pp. 58-70
Author(s):  
Leila Khiari ◽  
Tahar Boudjedaa ◽  
Abdenacer Makhlouf ◽  
Mohammed Tayeb Meftah
Keyword(s):  
Phase Space ◽  
Path Integral ◽  
Adiabatic Approximation ◽  
Berry Phase ◽  
Quadratic System ◽  
Harmonic Oscillators ◽  
Time Dependent ◽  
Noncommutative Phase Space ◽  
Integral Formalism ◽  
Coupled Harmonic Oscillators

The purpose of this paper is the description of Berry’s phase, in the Euclidean Path Integral formalism, for 2D quadratic system: two time dependent coupled harmonic oscillators. This treatment is achieved by using the adiabatic approximation in the commutative and noncommutative phase space

Autonomous Geometrical Mechanics

2018 ◽  
Author(s):  
Peter Mann
Keyword(s):  
Phase Space ◽  
Contact Structure ◽  
Invariant Tori ◽  
Time Dependent ◽  
Contact Structures ◽  
Natural Setting ◽  
Adiabatic Invariance ◽  
Jet Bundle ◽  
Integrability Theorem ◽  
Extended Phase

This chapter examines the structure of the phase space of an integrable system as being constructed from invariant tori using the Arnold–Liouville integrability theorem, and periodic flow and ergodic flow are investigated using action-angle theory. Time-dependent mechanics is formulated by extending the symplectic structure to a contact structure in an extended phase space before it is shown that mechanics has a natural setting on a jet bundle. The chapter then describes phase space of integrable systems and how tori behave when time-dependent dynamics occurs. Adiabatic invariance is discussed, as well as slow and fast Hamiltonian systems, the Hannay angle and counter adiabatic terms. In addition, the chapter discusses foliation, resonant tori, non-resonant tori, contact structures, Pfaffian forms, jet manifolds and Stokes’s theorem.

scholarly journals Time-dependent relaxed magnetohydrodynamics: Inclusion of cross helicity constraint using phase-space action

2020 ◽  
Vol 27 (6) ◽  
pp. 062504 ◽  
Author(s):  
R. L. Dewar ◽  
J. W. Burby ◽  
Z. S. Qu ◽  
N. Sato ◽  
M. J. Hole
Keyword(s):  
Phase Space ◽  
Time Dependent ◽  
Space Action
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