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.

scholarly journals A VARIATIONAL FORMULATION OF SYMPLECTIC NONCOMMUTATIVE MECHANICS

2007 ◽  
Vol 04 (05) ◽  
pp. 789-805 ◽  
Author(s):  
IGNACIO CORTESE ◽  
J. ANTONIO GARCÍA
Keyword(s):  
Dynamical System ◽  
Phase Space ◽  
Variational Principle ◽  
Configuration Space ◽  
Variational Formulation ◽  
Noncommutative Space ◽  
First Order ◽  
Dynamical Properties ◽  
Definition Of ◽  
Space Noncommutativity

The standard lore in noncommutative physics is the use of first order variational description of a dynamical system to probe the space noncommutativity and its consequences in the dynamics in phase space. As the ultimate goal is to understand the inherent space noncommutativity, we propose a variational principle for noncommutative dynamical systems in configuration space, based on results of our previous work [18]. We hope that this variational formulation in configuration space can be of help to elucidate the definition of some global and dynamical properties of classical and quantum noncommutative space.

scholarly journals NONCOMMUTATIVE SPACE CORRECTIONS ON THE KLEIN–GORDON AND DIRAC OSCILLATORS SPECTRA

2011 ◽  
Vol 26 (29) ◽  
pp. 4991-5003 ◽  
Author(s):  
ROBERTO V. MALUF
Keyword(s):  
Perturbation Theory ◽  
Energy Levels ◽  
Zeeman Splitting ◽  
Nonrelativistic Limit ◽  
Order Perturbation ◽  
Noncommutative Space ◽  
First Order ◽  
Commutative Space ◽  
Klein Gordon ◽  
First Order Perturbation

We consider the influence of a noncommutative space on the Klein–Gordon and the Dirac oscillators. The nonrelativistic limit is taken and the θ-modified Hamiltonians are determined. The corrections of these Hamiltonians on the energy levels are evaluated in first-order perturbation theory. It is observed a total lifting of the degeneracy to the considered levels. Such effects are similar to the Zeeman splitting in a commutative space.

DKP oscillator in noncommutative phase space

2009 ◽  
Vol 87 (9) ◽  
pp. 989-993 ◽  
Author(s):  
Guangjie Guo ◽  
Chaoyun Long ◽  
Zuhua Yang ◽  
Shuijie Qin
Keyword(s):  
Energy Spectrum ◽  
Phase Space ◽  
Exact Solutions ◽  
Nonrelativistic Limit ◽  
Noncommutative Phase Space

The exact solutions of the Duffin–Kemmer–Petiau (DKP) oscillator for spin-0 particles have been studied in noncommutative phase space. The results show that due to the noncommutative effect, the energy spectrum of the DKP oscillator for spin-0 particles is no longer degenerate. In addition, we obtain the nonrelativistic limit of the energy spectrum.

scholarly journals ON THE THREE-DIMENSIONAL PAULI EQUATION IN NONCOMMUTATIVE PHASE-SPACE

2021 ◽  
Vol 61 (1) ◽  
pp. 230-241
Author(s):  
Ilyas Haouam
Keyword(s):  
Phase Space ◽  
Continuity Equation ◽  
Helmholtz Free Energy ◽  
Three Dimensional ◽  
Noncommutative Phase Space ◽  
Pauli Equation ◽  
Knowing That ◽  
The One ◽  
Magnetization Current ◽  
Space Noncommutativity

In this paper, we obtained the three-dimensional Pauli equation for a spin-1/2 particle in the presence of an electromagnetic field in a noncommutative phase-space as well as the corresponding deformed continuity equation, where the cases of a constant and non-constant magnetic fields are considered. Due to the absence of the current magnetization term in the deformed continuity equation as expected, we had to extract it from the noncommutative Pauli equation itself without modifying the continuity equation. It is shown that the non-constant magnetic field lifts the order of the noncommutativity parameter in both the Pauli equation and the corresponding continuity equation. However, we successfully examined the effect of the noncommutativity on the current density and the magnetization current. By using a classical treatment, we derived the semi-classical noncommutative partition function of the three-dimensional Pauli system of the one-particle and N-particle systems. Then, we employed it for calculating the corresponding Helmholtz free energy followed by the magnetization and the magnetic susceptibility of electrons in both commutative and noncommutative phase-spaces. Knowing that with both the three-dimensional Bopp-Shift transformation and the Moyal-Weyl product, we introduced the phase-space noncommutativity in the problems in question.

Phase–space noncommutativity and the thermodynamics of the Landau system

2017 ◽  
Vol 32 (20) ◽  
pp. 1750102
Author(s):  
Aslam Halder ◽  
Sunandan Gangopadhyay
Keyword(s):  
Phase Space ◽  
Partition Function ◽  
Equivalent System ◽  
Noncommutative Phase Space ◽  
Nc System ◽  
Space Noncommutativity

Thermodynamics of the Landau system in noncommutative phase–space (NCPS) has been studied in this paper. The analysis involves the use of generalized Bopp-shift transformations to map the noncommutative (NC) system to its commutative equivalent system. The partition function of the system is computed and from this, the magnetization and the susceptibility of the Landau system are obtained. The results reveal that the magnetization and the susceptibility get modified by both the spatial and momentum NC parameters [Formula: see text] and [Formula: see text]. We then investigate the de Hass–van Alphen effect in NCPS. Here, the oscillation of the magnetization and the susceptibility get corrected by both the spatial and momentum NC parameters [Formula: see text] and [Formula: see text].

scholarly journals Zeeman Effect in Phase Space

2020 ◽  
Vol 2020 ◽  
pp. 1-9
Author(s):  
R. A. S. Paiva ◽  
R. G. G. Amorim ◽  
S. C. Ulhoa ◽  
A. E. Santana ◽  
F. C. Khanna
Keyword(s):  
Magnetic Field ◽  
Perturbation Theory ◽  
Phase Space ◽  
External Magnetic Field ◽  
Hydrogen Atom ◽  
Schrödinger Equation ◽  
Harmonic Oscillator ◽  
Schrodinger Equation ◽  
Zeeman Effect ◽  
Two Dimensional

The two-dimensional hydrogen atom in an external magnetic field is considered in the context of phase space. Using the solution of the Schrödinger equation in phase space, the Wigner function related to the Zeeman effect is calculated. For this purpose, the Bohlin mapping is used to transform the Coulomb potential into a harmonic oscillator problem. Then, it is possible to solve the Schrödinger equation easier by using the perturbation theory. The negativity parameter for this system is realised.

Hydrogen Atom Spectrum in Noncommutative Phase Space

2006 ◽  
Vol 23 (5) ◽  
pp. 1122-1123 ◽  
Author(s):  
Li Kang ◽  
Nidal Chamoun
Keyword(s):  
Phase Space ◽  
Hydrogen Atom ◽  
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 Two-Dimensional Pauli Equation in Noncommutative Phase-Space

2021 ◽  
Vol 66 (9) ◽  
pp. 771
Author(s):  
I. Haouam
Keyword(s):  
Magnetic Field ◽  
Phase Space ◽  
Classical Limit ◽  
Helmholtz Free Energy ◽  
Particle Systems ◽  
Two Dimensional ◽  
Noncommutative Phase Space ◽  
Pauli Equation ◽  
The Impact ◽  
Space Noncommutativity

We study the Pauli equation in a two-dimensional noncommutative phase-space by considering a constant magnetic field perpendicular to the plane. The noncommutative problem is related to the equivalent commutative one through a set of two-dimensional Bopp-shift transformations. The energy spectrum and the wave function of the two-dimensional noncommutative Pauli equation are found, where the problem in question has been mapped to the Landau problem. In the classical limit, we have derived the noncommutative semiclassical partition function for one- and N- particle systems. The thermodynamic properties such as the Helmholtz free energy, mean energy, specific heat and entropy in noncommutative and commutative phasespaces are determined. The impact of the phase-space noncommutativity on the Pauli system is successfully examined.

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