Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

e-Gnosis

NONCOMMUTATIVE HARMONIC OSCILLATOR, ENTROPY AND ENTANGLEMENT

P.B. Espinoza, Armando Gallegos

Published Jan 1, 2010• 0 citations
OpenAlex

Abstract

We show that the time evolution of the two dimensional noncommutative harmonic oscillator gives rise to entanglement. This is achieved at the level of the evolution operator by using the algebraic approach. The measure of entropy and the states of maximum entanglement are also considered in this context.

Related papers

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

Fethi Madouri, Abdeldjalil Merdaci

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 [Formula: see text] 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.

International Journal of Modern Physics B•Jul 14, 2022•1 citation

ENTANGLED STATE REPRESENTATIONS IN NONCOMMUTATIVE PHASE SPACE

Guangjie Guo, Chao‐Yun Long, Shuijie Qin +2 more

The entangled state representation has been constructed on noncommutative phase space. Using this appropriate representation, the energy spectrum of general two-dimensional harmonic oscillator has been obtained exactly.

International Journal of Modern Physics A•Oct 20, 2009•0 citations

Collapse-revival of entanglement in a two-dimensional noncommutative harmonic oscillator: A Schmidt modes analysis

Tarek Sbeouelji, Abdeldjalil Merdaci, Fethi Madouri

In this paper, we study the dynamics of entanglement in a two-dimensional noncommutative harmonic oscillator. With the help of the so-called Bopp shift, we map the Hamiltonian describing the system into an equivalent commutative form. This brings into play a Schwinger realization of the SU(2) Lie algebra. Subsequently, we derive the time-dependent number state wave functions. Then, we use the Schmidt modes decomposition together with the notion of purity to derive explicitly the amount of entanglement encoded in the most general accessible configurations of pairwise states. In doing so, we show that there is an intimate connection between the non-commutativity parameter and the phenomenon of collapse and revival of entanglement exhibited by the system.

Modern Physics Letters A•Jul 4, 2025•0 citations

REPRESENTATION OF NONCOMMUTATIVE PHASE SPACE

KANG LI, JIANHUA WANG, CHIYI CHEN

The representations of the algebra of coordinates and momenta of noncommutative phase space are given. We study, as an example, the harmonic oscillator in noncommutative space of any dimension. Finally the map of Schrödinger equation from noncommutative space to commutative space is obtained.

arXiv:hep-th/0409234•Modern Physics Letters A•Aug 24, 2005•73 citations

Entanglement dynamics in short- and long-range harmonic oscillators

M. Ghasemi Nezhadhaghighi, M. A. Rajabpour

We study the time evolution of the entanglement entropy in the short- and long-range-coupled harmonic oscillators that have well-defined continuum limit field theories. We first introduce a method to calculate the entanglement evolution in generic coupled harmonic oscillators after quantum quench. Then we study the entanglement evolution after quantum quench in harmonic systems in which the couplings decay effectively as $1/{r}^{d+\ensuremath{\alpha}}$ with the distance $r$. After quenching the mass from a nonzero value to zero we calculate numerically the time evolution of von Neumann and R\'enyi entropies. We show that for $1<\ensuremath{\alpha}<2$ we have a linear growth of entanglement and then saturation independent of the initial state. For $0<\ensuremath{\alpha}<1$ depending on the initial state we can have logarithmic growth or just fluctuation of entanglement. We also calculate the mutual information dynamics of two separated individual harmonic oscillators. Our findings suggest that in our system there is no particular connection between having a linear growth of entanglement after quantum quench and having a maximum group velocity or generalized Lieb-Robinson bound.

arXiv:1408.3744•Physical Review B•Nov 26, 2014•87 citations

DEFORMED HARMONIC OSCILLATOR AND NONLINEAR COHERENT STATES: NONCOMMUTATIVE QUANTUM SPACE APPROACH

M. H. Naderi, M. Soltanolkotabi, R. Roknizadeh

In this paper, by using the Wess–Zumino formalism of noncommutative differential calculus, we show that the concept of nonlinear coherent states originates from noncommutative geometry. For this purpose, we first formulate the differential calculus on a GL p, q(2) quantum plane. By using the commutation relations between coordinates and their interior derivatives, we then construct the two-parameter (p, q)-deformed quantum phase space together with the associated deformed Heisenberg commutation relations. Finally, by applying the obtained results for the quantum harmonic oscillator we construct the associated coherent states, which can be identified as nonlinear coherent states. Furthermore, we show that some of the well-known deformed (nonlinear) coherent states, such as two-parameter (p, q)-deformed coherent states, Maths-type q-deformed coherent states, Phys-type q-deformed coherent states and Quesne deformed coherent states, can be easily obtained from our treatment.

International Journal of Modern Physics A•Apr 15, 2009•4 citations
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 [Formula: see text] 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.
In this paper, we study the dynamics of entanglement in a two-dimensional noncommutative harmonic oscillator. With the help of the so-called Bopp shift, we map the Hamiltonian describing the system into an equivalent commutative form. This brings into play a Schwinger realization of the SU(2) Lie algebra. Subsequently, we derive the time-dependent number state wave functions. Then, we use the Schmidt modes decomposition together with the notion of purity to derive explicitly the amount of entanglement encoded in the most general accessible configurations of pairwise states. In doing so, we show that there is an intimate connection between the non-commutativity parameter and the phenomenon of collapse and revival of entanglement exhibited by the system.
We study the time evolution of the entanglement entropy in the short- and long-range-coupled harmonic oscillators that have well-defined continuum limit field theories. We first introduce a method to calculate the entanglement evolution in generic coupled harmonic oscillators after quantum quench. Then we study the entanglement evolution after quantum quench in harmonic systems in which the couplings decay effectively as $1/{r}^{d+\ensuremath{\alpha}}$ with the distance rrr. After quenching the mass from a nonzero value to zero we calculate numerically the time evolution of von Neumann and R\'enyi entropies. We show that for $1<\ensuremath{\alpha}<2$ we have a linear growth of entanglement and then saturation independent of the initial state. For $0<\ensuremath{\alpha}<1$ depending on the initial state we can have logarithmic growth or just fluctuation of entanglement. We also calculate the mutual information dynamics of two separated individual harmonic oscillators. Our findings suggest that in our system there is no particular connection between having a linear growth of entanglement after quantum quench and having a maximum group velocity or generalized Lieb-Robinson bound.
In this paper, by using the Wess–Zumino formalism of noncommutative differential calculus, we show that the concept of nonlinear coherent states originates from noncommutative geometry. For this purpose, we first formulate the differential calculus on a GL p, q(2) quantum plane. By using the commutation relations between coordinates and their interior derivatives, we then construct the two-parameter (p, q)-deformed quantum phase space together with the associated deformed Heisenberg commutation relations. Finally, by applying the obtained results for the quantum harmonic oscillator we construct the associated coherent states, which can be identified as nonlinear coherent states. Furthermore, we show that some of the well-known deformed (nonlinear) coherent states, such as two-parameter (p, q)-deformed coherent states, Maths-type q-deformed coherent states, Phys-type q-deformed coherent states and Quesne deformed coherent states, can be easily obtained from our treatment.