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.

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.

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.

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].

DKP Oscillator with Spin-0 in Three-dimensional Noncommutative Phase Space

2010 ◽  
Vol 49 (3) ◽  
pp. 644-651 ◽  
Author(s):  
Zu-Hua Yang ◽  
Chao-Yun Long ◽  
Shuei-Jie Qin ◽  
Zheng-Wen Long
Keyword(s):  
Phase Space ◽  
Three Dimensional ◽  
Noncommutative Phase Space

MECHANICAL STICK-SLIP VIBRATIONS

1995 ◽  
Vol 05 (03) ◽  
pp. 637-651 ◽  
Author(s):  
U. GALVANETTO ◽  
S.R. BISHOP ◽  
L. BRISEGHELLA
Keyword(s):  
Phase Space ◽  
Three Dimensional ◽  
Basins Of Attraction ◽  
Global Dynamics ◽  
Chaotic Oscillations ◽  
Stick Slip ◽  
One Dimensional ◽  
Dimensional Phase Space ◽  
The One ◽  
Two Degree Of Freedom

In this paper we consider the behavior of a two degree-of-freedom mechanical system incorporating static and dynamic friction, assumed to be a decreasing function of the relative sliding velocity. The model consists of two blocks linked by springs, which ride upon a moving belt. The dynamics of the system are described within a four-dimensional phase space. A three-dimensional Poincaré map is discussed together with a simpler one-dimensional map of a scalar variable. Considering the one-dimensional map it is possible to study all the attractors of the system for small belt velocities including the construction of one-dimensional basins of attraction. Thus, albeit in a partial zone of the control-phase space, the global dynamics of the system can be characterized displaying periodic, quasi-periodic and chaotic oscillations.

scholarly journals ANALYTICAL SOLUTION OF (2+1) DIMENSIONAL DIRAC EQUATION IN TIME-DEPENDENT NONCOMMUTATIVE PHASE-SPACE

2020 ◽  
Vol 60 (2) ◽  
pp. 111-121
Author(s):  
Ilyas Haouam
Keyword(s):  
Phase Space ◽  
Dirac Equation ◽  
Analytical Solution ◽  
General Solution ◽  
Time Dependent ◽  
Noncommutative Phase Space ◽  
Invariant Method ◽  
Knowing That ◽  
Dirac Hamiltonian

In this article, we studied the system of a (2+1) dimensional Dirac equation in a time-dependent noncommutative phase-space. More specifically, we investigated the analytical solution of the corresponding system by the Lewis-Riesenfeld invariant method based on the construction of the Lewis-Riesenfeld invariant. Knowing that we obtained the time-dependent Dirac Hamiltonian of the problem in question from a time-dependent Bopp-Shift translation, then used it to set the Lewis- Riesenfeld invariant operators. Thereafter, the obtained results were used to express the eigenfunctions that lead to determining the general solution of the system.

THREE-DIMENSIONAL KLEIN–GORDON OSCILLATOR IN A BACKGROUND MAGNETIC FIELD IN NONCOMMUTATIVE PHASE SPACE

2012 ◽  
Vol 27 (10) ◽  
pp. 1250047 ◽  
Author(s):  
MAI-LIN LIANG ◽  
RUI-LIN YANG
Keyword(s):  
Magnetic Field ◽  
Phase Space ◽  
Coherent States ◽  
Semiclassical Limit ◽  
Equations Of Motion ◽  
Three Dimensional ◽  
Noncommutative Phase Space ◽  
Background Magnetic Field ◽  
Klein Gordon ◽  
Lowering Operators

In noncommutative phase space, wave functions and energy spectra are derived for the three-dimensional (3D) Klein–Gordon oscillator in a background magnetic field. The raising and lowering operators for this system are derived from the Heisenberg equations of motion for a 3D nonrelativistic oscillator. The coherent states are obtained as the eigenstates of the lowering operators and it is found that the coherent states are not the minimum uncertainty states due to the noncommutativity of the space. It is also pointed out that in the semiclassical limit, quantum matrix elements give solutions to the semiclassical equations.

Diffraction contrast of dislocations in icosahedral quasicrystals

1990 ◽  
Vol 48 (4) ◽  
pp. 454-455
Author(s):  
K. Urban ◽  
Z. Zhang ◽  
M. Wollgarten ◽  
D. Gratias
Keyword(s):  
Dimensional Space ◽  
Three Dimensional ◽  
Complete Characterization ◽  
Extinction Condition ◽  
Burgers Vector ◽  
Diffraction Contrast ◽  
Lattice Geometry ◽  
Reference Space ◽  
Icosahedral Quasicrystals ◽  
The One

Recently dislocations have been observed by electron microscopy in the icosahedral quasicrystalline (IQ) phase of Al65Cu20Fe15. These dislocations exhibit diffraction contrast similar to that known for dislocations in conventional crystals. The contrast becomes extinct for certain diffraction vectors g. In the following the basis of electron diffraction contrast of dislocations in the IQ phase is described. Taking account of the six-dimensional nature of the Burgers vector a “strong” and a “weak” extinction condition are found.Dislocations in quasicrystals canot be described on the basis of simple shear or insertion of a lattice plane only. In order to achieve a complete characterization of these dislocations it is advantageous to make use of the one to one correspondence of the lattice geometry in our three-dimensional space (R3) and that in the six-dimensional reference space (R6) where full periodicity is recovered . Therefore the contrast extinction condition has to be written as gpbp + gobo = 0 (1). The diffraction vector g and the Burgers vector b decompose into two vectors gp, bp and go, bo in, respectively, the physical and the orthogonal three-dimensional sub-spaces of R6.

Exploring the Multidimensional Facets of Authoritarianism: Authoritarian Aggression and Social Dominance Orientation

2008 ◽  
Vol 67 (1) ◽  
pp. 51-60 ◽  
Author(s):  
Stefano Passini
Keyword(s):  
Social Dominance ◽  
Factor Model ◽  
Three Dimensional ◽  
Social Dominance Orientation ◽  
Model Fit ◽  
Regression Analyses ◽  
One Dimensional ◽  
Confirmatory Factor ◽  
The One ◽  
Better Than

The relation between authoritarianism and social dominance orientation was analyzed, with authoritarianism measured using a three-dimensional scale. The implicit multidimensional structure (authoritarian submission, conventionalism, authoritarian aggression) of Altemeyer’s (1981, 1988) conceptualization of authoritarianism is inconsistent with its one-dimensional methodological operationalization. The dimensionality of authoritarianism was investigated using confirmatory factor analysis in a sample of 713 university students. As hypothesized, the three-factor model fit the data significantly better than the one-factor model. Regression analyses revealed that only authoritarian aggression was related to social dominance orientation. That is, only intolerance of deviance was related to high social dominance, whereas submissiveness was not.

Sea Urchins and Circuses: The Modernist Natural Histories of Jean Painlevé and Alexander Calder

2018 ◽  
Vol 13 (2) ◽  
pp. 187-211
Author(s):  
Patricia E. Chu
Keyword(s):  
New Media ◽  
Sea Urchins ◽  
Life Sciences ◽  
Three Dimensional ◽  
Machine Age ◽  
Avant Garde ◽  
History Of ◽  
And Performance ◽  
The One ◽  
Natural Historian

The Paris avant-garde milieu from which both Cirque Calder/Calder's Circus and Painlevé’s early films emerged was a cultural intersection of art and the twentieth-century life sciences. In turning to the style of current scientific journals, the Paris surrealists can be understood as engaging the (life) sciences not simply as a provider of normative categories of materiality to be dismissed, but as a companion in apprehending the “reality” of a world beneath the surface just as real as the one visible to the naked eye. I will focus in this essay on two modernist practices in new media in the context of the history of the life sciences: Jean Painlevé’s (1902–1989) science films and Alexander Calder's (1898–1976) work in three-dimensional moving art and performance—the Circus. In analyzing Painlevé’s work, I discuss it as exemplary of a moment when life sciences and avant-garde technical methods and philosophies created each other rather than being classified as separate categories of epistemological work. In moving from Painlevé’s films to Alexander Calder's Circus, Painlevé’s cinematography remains at the forefront; I use his film of one of Calder's performances of the Circus, a collaboration the men had taken two decades to complete. Painlevé’s depiction allows us to see the elements of Calder's work that mark it as akin to Painlevé’s own interest in a modern experimental organicism as central to the so-called machine-age. Calder's work can be understood as similarly developing an avant-garde practice along the line between the bestiary of the natural historian and the bestiary of the modern life scientist.

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