Exact Solution of (2+1)-Dimensional Noncommutative Pauli Equation in a Time-Dependent Background

Haouam, Ilyas; Hassanabadi, H.

doi:10.1007/s10773-022-05197-5

Cited by 11 publications

(3 citation statements)

References 56 publications

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“…Various forms of NC spaces have been explored, see Refs. [31][32][33][34][35][36][37] for an overview. However, one type is particularly important to us, in which the noncommutativity of space is position dependent, called dynamical NC (DNC) space.…”

Section: Of 16mentioning

confidence: 99%

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Landau Problem in Dynamical Noncommutative Space

Haouam,

Alavi

2023

Preprint

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This paper aims to investigate the Landau problem within a two-dimensional dynamical noncommutative (DNC) space. We address the deformed Landau problem using time-independent perturbation theory, where the eigenenergies are successfully determined. Notably, the energy shift depends on the DNC parameter τ . Using the accuracy of energy measurement, we put an upper bound on the parameter τ . Moreover, we study magnetoconductivity by employing the Kubo formula. This approach has allowed us to test the effects of noncommutative and DNC spaces on the behavior of magnetoconductivity. We show that dynamical noncommutativity of space has no effects on the x-component of the conductivity.

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Section: Of 16mentioning

confidence: 99%

“…but, as long as Θ is very small, therefore we use the series expansion 1 + Θ Using the above two-equations ( 29), (31), the Pauli equation reads…”

Section: B Unperturbed Systemmentioning

confidence: 99%

Landau Problem in Dynamical Noncommutative Space

Haouam,

Alavi

2023

Preprint

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“…Also, it is worth noting that different types of phase-space noncommutativity have been considered (see Refs. [29][30][31][32] for an overview). The transition between the commutative setting and the NC one, or vice versa, involves four essential methods: (i) Moyal-Weyl product (⋆product) instead of the ordinary product for actions and physical systems functions, (ii) Weyl-Wigner maps, which utilize the ordinary product alongside Weyl operators.…”

Section: Introductionmentioning

confidence: 99%

The Effect of Noncommutative Phase-Space, Local and Nonlocal Potentials on the Current Density in the Context of Minimal Uncertainty in Momentum

Haouam

2024

Preprint

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In this article, we investigate both the Schrödinger and continuity equations in the presence of nonlocal potential that arising from electron-electron interaction and local one in the context of minimal uncertainty in momentum within commutative and noncommutative frameworks. Furthermore, the Frahn–Lemmer potential type is used. Interestingly, the combined effects of both the phase-space noncommutativity and nonlocality on the current density while considering a minimal uncertainty in momentum are examined. We find that the current density, as conventionally defined, does not fulfil the condition of current conservation, thus, a new definition of the current density that encompasses the aforementioned contributions is given. Thereafter, it is shown that the computed current using the new definition of the current density satisfies the current conservation. Noting that using both the ★ product and linear Bopp-Shift, the noncommutativity is inserted.

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Foldy–Wouthuysen Transformation of Noncommutative Dirac Equation in the Presence of Minimal Uncertainty in Momentum

Haouam

2023

Few-Body Syst

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Exact Solution of (2+1)-Dimensional Noncommutative Pauli Equation in a Time-Dependent Background

Cited by 11 publications

References 56 publications

Landau Problem in Dynamical Noncommutative Space

Landau Problem in Dynamical Noncommutative Space

The Effect of Noncommutative Phase-Space, Local and Nonlocal Potentials on the Current Density in the Context of Minimal Uncertainty in Momentum

Foldy–Wouthuysen Transformation of Noncommutative Dirac Equation in the Presence of Minimal Uncertainty in Momentum

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