scholarly journals Upper bound on the momentum scale in noncommutative phase space of canonical type

2019 ◽  
Vol 127 (2) ◽  
pp. 20008 ◽  
Author(s):  
Kh. P. Gnatenko ◽  
V. M. Tkachuk
Keyword(s):  
Phase Space ◽  
Upper Bound ◽  
Noncommutative Phase Space ◽  
Momentum Scale ◽  
Canonical Type

scholarly journals Effect of noncommutativity on the spectrum of free particle and harmonic oscillator in rotationally invariant noncommutative phase space

2018 ◽  
Vol 33 (16) ◽  
pp. 1850091 ◽  
Author(s):  
Kh. P. Gnatenko ◽  
O. V. Shyiko
Keyword(s):  
Phase Space ◽  
Harmonic Oscillator ◽  
Rotational Symmetry ◽  
Free Particle ◽  
Second Order ◽  
Noncommutative Phase Space ◽  
Noncommutative Algebra ◽  
Ordinary Space ◽  
Canonical Type ◽  
Rotationally Invariant

We consider rotationally invariant noncommutative algebra with tensors of noncommutativity constructed with the help of additional coordinates and momenta. The algebra is equivalent to the well-known noncommutative algebra of canonical type. In the noncommutative phase space, rotational symmetry influence of noncommutativity on the spectrum of free particle and the spectrum of harmonic oscillator is studied up to the second-order in the parameters of noncommutativity. We find that because of momentum noncommutativity, the spectrum of free particle is discrete and corresponds to the spectrum of harmonic oscillator in the ordinary space (space with commutative coordinates and commutative momenta). We obtain the spectrum of the harmonic oscillator in the rotationally invariant noncommutative phase space and conclude that noncommutativity of coordinates affects its mass. The frequency of the oscillator is affected by the coordinate noncommutativity and the momentum noncommutativity. On the basis of the results, the eigenvalues of squared length operator are found and restrictions on the value of length in noncommutative phase space with rotational symmetry are analyzed.

scholarly journals Features of free particles system motion in noncommutative phase space and conservation of the total momentum

2018 ◽  
Vol 33 (23) ◽  
pp. 1850131 ◽  
Author(s):  
Kh. P. Gnatenko ◽  
H. P. Laba ◽  
V. M. Tkachuk
Keyword(s):  
Phase Space ◽  
Composite System ◽  
Free Particle ◽  
Total Momentum ◽  
Initial Moment ◽  
Integrals Of Motion ◽  
Integral Of Motion ◽  
Noncommutative Phase Space ◽  
Free Particles ◽  
Canonical Type

Influence of noncommutativity on the motion of composite system is studied in noncommutative phase space of canonical type. A system composed by N free particles is examined. We show that because of the momentum noncommutativity free particles of different masses with the same velocities at the initial moment of time do not move together. The trajectory and the velocity of a free particle in noncommutative phase space depend on its mass. So, a system of the free particles flies away. Also, it is shown that the total momentum defined in the traditional way is not integral of motion in a space with noncommutativity of coordinates and noncommutativity of momenta. We find that in the case when parameters of noncommutativity corresponding to a particle are determined by its mass, the trajectory and the velocity of the free particles are independent of the mass. Also, the total momenta as integrals of motion can be introduced in noncommutative phase space.

scholarly journals Noncommutative phase space with rotational symmetry and hydrogen atom

2017 ◽  
Vol 32 (26) ◽  
pp. 1750161 ◽  
Author(s):  
Kh. P. Gnatenko ◽  
V. M. Tkachuk
Keyword(s):  
Phase Space ◽  
Hydrogen Atom ◽  
Rotational Symmetry ◽  
Energy Levels ◽  
Upper Bounds ◽  
Second Order ◽  
Noncommutative Phase Space ◽  
Noncommutative Algebra ◽  
Canonical Type ◽  
Rotationally Invariant

We construct algebra with noncommutativity of coordinates and noncommutativity of momenta which is rotationally invariant and equivalent to noncommutative algebra of canonical type. Influence of noncommutativity on the energy levels of hydrogen atom is studied in rotationally invariant noncommutative phase space. We find corrections to the levels up to the second order in the parameters of noncommutativity and estimate the upper bounds of these parameters.

scholarly journals Algebraic Approach to Exact Solution of the (2 + 1)-Dimensional Dirac Oscillator in the Noncommutative Phase Space

2017 ◽  
Vol 2017 ◽  
pp. 1-6
Author(s):  
H. Panahi ◽  
A. Savadi
Keyword(s):  
Exact Solution ◽  
Phase Space ◽  
Algebraic Approach ◽  
Wave Functions ◽  
Dirac Oscillator ◽  
Noncommutative Phase Space ◽  
Energy Eigenvalues ◽  
Good Agreement

We study the (2 + 1)-dimensional Dirac oscillator in the noncommutative phase space and the energy eigenvalues and the corresponding wave functions of the system are obtained through the sl(2) algebraization. It is shown that the results are in good agreement with those obtained previously via a different method.

scholarly journals TRACE OF PHASE-SPACE NONCOMMUTATIVITY IN RESPONSE OF A FREE PARTICLE TO LINEARIZED GRAVITATIONAL WAVES

2013 ◽  
Vol 28 (35) ◽  
pp. 1350161 ◽  
Author(s):  
SUNANDAN GANGOPADHYAY ◽  
ANIRBAN SAHA ◽  
SWARUP SAHA
Keyword(s):  
Phase Space ◽  
Gravitational Waves ◽  
Cross Correlation ◽  
Free Particle ◽  
Momentum Scale ◽  
Specific Frequency ◽  
Global Nature ◽  
Space Noncommutativity ◽  
Correlation Procedure ◽  
Noncommutative Parameter

Interaction of linearized gravitational waves with a otherwise free particle has been studied quantum mechanically in a noncommutative (NC) phase-space to examine whether the particle's response to the gravitational wave gets modified due to spatial and/or momentum noncommutativity. The result shows that momentum noncommutativity introduces a oscillatory noise with a specific frequency determined by the fundamental momentum scale and particle mass. Because of the global nature of the phase-space noncommutativity such noise will have similar characteristics for all detector sites and thus will stand out in a data cross-correlation procedure. If detected, this noise will provide evidence of momentum noncommutativity and also an estimation of the relevant noncommutative parameter.

scholarly journals Composite system in rotationally invariant noncommutative phase space

2018 ◽  
Vol 33 (07) ◽  
pp. 1850037 ◽  
Author(s):  
Kh. P. Gnatenko ◽  
V. M. Tkachuk
Keyword(s):  
Phase Space ◽  
Composite System ◽  
Particle System ◽  
Rotational Symmetry ◽  
Center Of Mass ◽  
Noncommutative Space ◽  
Effective Parameters ◽  
Noncommutative Phase Space ◽  
Noncommutative Algebra ◽  
Rotationally Invariant

Composite system is studied in noncommutative phase space with preserved rotational symmetry. We find conditions on the parameters of noncommutativity on which commutation relations for coordinates and momenta of the center-of-mass of composite system reproduce noncommutative algebra for coordinates and momenta of individual particles. Also, on these conditions, the coordinates and the momenta of the center-of-mass satisfy noncommutative algebra with effective parameters of noncommutativity which depend on the total mass of the system and do not depend on its composition. Besides, it is shown that on these conditions the coordinates in noncommutative space do not depend on mass and can be considered as kinematic variables, the momenta are proportional to mass as it has to be. A two-particle system with Coulomb interaction is studied and the corrections to the energy levels of the system are found in rotationally invariant noncommutative phase space. On the basis of this result the effect of noncommutativity on the spectrum of exotic atoms is analyzed.

scholarly journals Thermodynamical properties of graphene in noncommutative phase–space

2014 ◽  
Vol 349 ◽  
pp. 402-410 ◽  
Author(s):  
Victor Santos ◽  
R.V. Maluf ◽  
C.A.S. Almeida
Keyword(s):  
Phase Space ◽  
Noncommutative Phase Space ◽  
Thermodynamical Properties
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