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On the collapse revival of entanglement in a two-dimensional noncommutative harmonic oscillator: An algebraic approach

Département de Physique, Laboratoire Matériaux et Fluides, Institut Préparatoire aux Etudes d’Ingénieurs de Tunis, Université de Tunis, 02 Rue J Lal Nehru, 1089 Montfleury, Tunis, Tunisia

E-mail Address: fethi.madouri@ipeit.rnu.tn

Corresponding author.

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Abdeldjalil Merdaci

Physics Department, Faculty of Sciences, University of 20 August 1955, Road El-Hadaiek, B.P. 26, 21000 Skikda, Algeria

E-mail Address: merdaci69abd@gmail.com

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https://doi.org/10.1142/S021797922250148XCited by:0 (Source: Crossref)

Abstract

In this paper, we employ an algebraic approach to investigate the dynamics of entanglement in a two-dimensional noncommutative harmonic oscillator. We start by using the so-called the Bopp shift to convert the Hamiltonian describing the system into an equivalent commutative one. This allows us to take advantage of the Schwinger oscillator construction of $S U (2)$ Lie algebra to reveal through the time evolution operator that there is a connection between the noncommutativity and entanglement. The degree of entanglement between the states is evaluated by using the purity function. The remarkable emerging feature is that, as long as the noncommutativity parameter is nonvanishing, the system exhibits the phenomenon of collapse and revival of entanglement.

Keywords:

PACS: 03.65.Fd, 03.65.Bg, 03.65.-w, 03.65.-d

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