scholarly journals Relativistic dispersion relation and putative metric structure in noncommutative phase-space

2019 ◽  
Vol 793 ◽  
pp. 240-246 ◽  
Author(s):  
P. Leal ◽  
O. Bertolami
Keyword(s):  
Phase Space ◽  
Dispersion Relation ◽  
Noncommutative Phase Space ◽  
Relativistic Dispersion

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.

Ion-cyclotron modes in weakly relativistic plasmas

1994 ◽  
Vol 51 (3) ◽  
pp. 371-379 ◽  
Author(s):  
Chandu Venugopal ◽  
P. J. Kurian ◽  
G. Renuka
Keyword(s):  
Dispersion Relation ◽  
High Frequency ◽  
Low Frequency ◽  
Dispersion Relations ◽  
The Other ◽  
Larmor Radius ◽  
Relativistic Plasmas ◽  
Ion Plasma ◽  
Maxwellian Plasma ◽  
Relativistic Dispersion

We derive a dispersion relation for the perpendicular propagation of ioncyclotron waves around the ion gyrofrequency ω+ in a weaklu relaticistic anisotropic Maxwellian plasma. These waves, with wavelength greater than the ion Larmor radius rL+ (k⊥ rL+ < 1), propagate in a plasma characterized by large ion plasma frequencies (). Using an ordering parameter ε, we separated out two dispersion relations, one of which is independent of the relativistic terms, while the other depends sensitively on them. The solutions of the former dispersion relation yield two modes: a low-frequency (LF) mode with a frequency ω < ω+ and a high-frequency (HF) mode with ω > ω+. The plasma is stable to the propagation of these modes. The latter dispersion relation yields a new LF mode in addition to the modes supported by the non-relativistic dispersion relation. The two LF modes can coalesce to make the plasma unstable. These results are also verified numerically using a standard root solver.

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

An Extra Phase for Two-Mode Coherent States Displaced in Noncommutative Phase Space

2012 ◽  
Vol 29 (4) ◽  
pp. 041102
Author(s):  
Long Yan ◽  
Xun-Li Feng ◽  
Zhi-Ming Zhang ◽  
Song-Hao Liu
Keyword(s):  
Phase Space ◽  
Coherent States ◽  
Noncommutative Phase Space

scholarly journals Relativistic Hydrogen-Like Atom on a Noncommutative Phase Space

2017 ◽  
Vol 56 (9) ◽  
pp. 2724-2737 ◽  
Author(s):  
Huseyin Masum ◽  
Sayipjamal Dulat ◽  
Mutallip Tohti
Keyword(s):  
Phase Space ◽  
Noncommutative Phase Space ◽  
Relativistic Hydrogen

scholarly journals Black hole thermodynamics in Snyder phase space

2017 ◽  
Vol 14 (11) ◽  
pp. 1750164
Author(s):  
Sara Saghafi ◽  
Kourosh Nozari
Keyword(s):  
Black Holes ◽  
Black Hole ◽  
Phase Space ◽  
Symplectic Structure ◽  
Symplectic Manifolds ◽  
Black Hole Thermodynamics ◽  
Schwarzschild Black Hole ◽  
Noncommutative Phase Space ◽  
Physics Of Black Holes ◽  
First Time

By defining a noncommutative symplectic structure, we study thermodynamics of Schwarzschild black hole in a Snyder noncommutative phase space for the first time. Since natural cutoffs are the results of compactness of symplectic manifolds in phase space, the physics of black holes in such a space would be affected mainly by these cutoffs. In this respect, this study provides a basis for more deeper understanding of the black hole thermodynamics in a pure mathematical viewpoint.

Phenomenology of noncommutative phase space via the anomalous Zeeman effect in hydrogen atom

2014 ◽  
Vol 29 (31) ◽  
pp. 1450177 ◽  
Author(s):  
Willien O. Santos ◽  
Andre M. C. Souza
Keyword(s):  
Phase Space ◽  
Hydrogen Atom ◽  
Zeeman Effect ◽  
Nonrelativistic Limit ◽  
Noncommutative Phase Space ◽  
G Factor ◽  
First Order ◽  
Anomalous Zeeman Effect ◽  
Space Noncommutativity ◽  
First Order Perturbation

The Hamiltonian describing the anomalous Zeeman effect for the hydrogen atom on noncommutative (NC) phase space is studied using the nonrelativistic limit of the Dirac equation. To preserve gauge invariance, space noncommutativity must be dropped. By using first-order perturbation theory, the correction to the energy is calculated for the case of a weak external magnetic field. We also obtained the orbital and spin g-factors on the NC phase space. We show that the experimental value for the spin g-factor puts an upper bound on the magnitude of the momentum NC parameter of the order of [Formula: see text], 34 μ eV /c. On the other hand, the experimental value for the spin g-factor was used to establish a correction introduced by NC phase space to the presently accepted value of Planck's constant with an uncertainty of 2 part in 1035.

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