scholarly journals Negative heat capacity for a Klein–Gordon oscillator in non-commutative complex phase space

2017 ◽  
Vol 14 (10) ◽  
pp. 1750141 ◽  
Author(s):  
Slimane Zaim ◽  
Hakim Guelmamene ◽  
Yazid Delenda
Keyword(s):  
Magnetic Field ◽  
Heat Capacity ◽  
Thermal Properties ◽  
Phase Space ◽  
Energy Levels ◽  
Two Dimensional ◽  
Complex Phase ◽  
First Order ◽  
Klein Gordon

We obtain exact solutions to the two-dimensional (2D) Klein–Gordon oscillator in a non-commutative (NC) complex phase space to first order in the non-commutativity parameter. We derive the exact NC energy levels and show that the energy levels split to [Formula: see text] levels. We find that the non-commutativity plays the role of a magnetic field interacting automatically with the spin of a particle induced by the non-commutativity of complex phase space. The effect of the non-commutativity parameter on the thermal properties is discussed. It is found that the dependence of the heat capacity [Formula: see text] on the NC parameter gives rise to a negative quantity. Phenomenologically, this effectively confirms the presence of the effects of self-gravitation induced by the non-commutativity of complex phase space.

Klein–Gordon oscillator in the presence of the minimal momentum

2019 ◽  
Vol 34 (25) ◽  
pp. 1950204 ◽  
Author(s):  
Won Sang Chung ◽  
Hassan Hassanabadi ◽  
Nasrin Farahani
Keyword(s):  
Magnetic Field ◽  
Uncertainty Principle ◽  
Energy Levels ◽  
Two Dimensional ◽  
Higher Dimensional ◽  
Klein Gordon ◽  
Extended Uncertainty ◽  
The Magnetic Field

In this paper, we use the higher-dimensional extended uncertainty principle to discuss the two-dimensional Klein–Gordon oscillator in the absence of the magnetic field and in the presence of the magnetic field. We find the energy levels with the extended uncertainty principle correction for two cases.

scholarly journals NONCOMMUTATIVE GRAPHENE

2013 ◽  
Vol 28 (16) ◽  
pp. 1350064 ◽  
Author(s):  
CATARINA BASTOS ◽  
ORFEU BERTOLAMI ◽  
NUNO COSTA DIAS ◽  
JOÃO NUNO PRATA
Keyword(s):  
Magnetic Field ◽  
External Magnetic Field ◽  
Dirac Equation ◽  
Energy Levels ◽  
Dirac Fermions ◽  
Two Dimensional ◽  
Dirac System ◽  
Noncommutative Parameter

We consider a noncommutative description of graphene. This description consists of a Dirac equation for massless Dirac fermions plus noncommutative corrections, which are treated in the presence of an external magnetic field. We argue that, being a two-dimensional Dirac system, graphene is particularly interesting to test noncommutativity. We find that momentum noncommutativity affects the energy levels of graphene and we obtain a bound for the momentum noncommutative parameter.

Invariance Groups in Classical and Quantum Mechanics

1973 ◽  
Vol 28 (3-4) ◽  
pp. 538-540 ◽  
Author(s):  
D. J. Simms
Keyword(s):  
Quantum Mechanics ◽  
Phase Space ◽  
Energy Levels ◽  
Classical Mechanics ◽  
Symmetry Groups ◽  
Casimir Invariants ◽  
Classical Phase Space ◽  
Invariance Groups ◽  
Classical And Quantum Mechanics

AbstractThis is a report on some new relations and analogies between classical mechanics and quantum mechanics which arise out of the work of Kostant and Souriau. Topics treated are i) the role of symmetry groups; ii) the notion of elementary system and the role of Casimir invariants; iii) energy levels; iv) quantisation in terms of geometric data on the classical phase space. Some applications are described.

Klein–Gordon oscillator with position-dependent mass in the rotating cosmic string spacetime

2018 ◽  
Vol 33 (04) ◽  
pp. 1850025 ◽  
Author(s):  
Bing-Qian Wang ◽  
Zheng-Wen Long ◽  
Chao-Yun Long ◽  
Shu-Rui Wu
Keyword(s):  
Magnetic Field ◽  
Cosmic String ◽  
Energy Levels ◽  
Homogeneous Magnetic Field ◽  
Spinless Particle ◽  
Klein Gordon ◽  
Coulomb Type ◽  
Dependent Mass ◽  
String Background ◽  
Position Dependent Mass

A spinless particle coupled covariantly to a uniform magnetic field parallel to the string in the background of the rotating cosmic string is studied. The energy levels of the electrically charged particle subject to the Klein–Gordon oscillator are analyzed. Afterwards, we consider the case of the position-dependent mass and show how these energy levels depend on the parameters in the problem. Remarkably, it shows that for the special case, the Klein–Gordon oscillator coupled covariantly to a homogeneous magnetic field with the position-dependent mass in the rotating cosmic string background has the similar behaviors to the Klein–Gordon equation with a Coulomb-type configuration in a rotating cosmic string background in the presence of an external magnetic field.

Effect of Brownian Motion and External Magnetic Field on the Effective Heat Capacity of Ferrofluids

2011 ◽  
Author(s):  
Narges Susan Mousavi Kh. ◽  
Sunil Kumar ◽  
Arvind Narayanaswamy
Keyword(s):  
Magnetic Field ◽  
Heat Capacity ◽  
Brownian Motion ◽  
Energy Equation ◽  
Volume Fraction ◽  
Physical Parameters ◽  
Effective Heat Capacity ◽  
Effective Heat ◽  
Negligible Contribution

An Eulerian formalism is used to derive the energy equation for a system of magnetic nanoparticles in a fluid (ferrofluid) in the presence of uniform magnetic field. The energy equation proposed here contains an effective heat capacity, which has contributions from: (1) Brownian motion of nanoparticles, (2) magnetic field, (3) temperature, and (4) volume fraction of particles. The modified term quantitatively shows the negligible contribution of the first three factors but the significant effect of concentration of particles in change in heat capacity of ferrofluid. In order to have a better understanding of the problem, the equation is converted to a non dimensional form from which the role of each of physical parameters can be inferred.

Quantization of coupled orbits in metals

1962 ◽  
Vol 270 (1340) ◽  
pp. 1-13 ◽  
Keyword(s):  
Magnetic Field ◽  
Perturbation Theory ◽  
Fourier Analysis ◽  
Level Density ◽  
Energy Levels ◽  
Interference Effects ◽  
Level System ◽  
First Order ◽  
Simple Network ◽  
First Order Perturbation

The failure of semi-elassical quantization of electron orbits in metals in the presence of a strong enough magnetic field (magnetic breakthrough) is discussed in an elementary fashion by means of first-order perturbation theory. The interference effects, which arise when orbits about different centres are coupled, are reproduced in a simple network analogue. Exact analysis of the network shows how the energy levels are broadened by the coupling and eventually reform into a different set of levels. Fourier analysis of the level density reveals what might be observed in the de Haas—van Alphen effect when magnetic breakthrough is significant, and it is concluded that in principle the whole evolution of the level system should be observable.

scholarly journals Spin-0 scalar particle interacts with scalar potential in the presence of magnetic field and quantum flux under the effects of KKT in 5D cosmic string spacetime

2020 ◽  
pp. 2150004
Author(s):  
Faizuddin Ahmed
Keyword(s):  
Magnetic Field ◽  
Quantum Dynamics ◽  
Bound States ◽  
Relativistic Quantum ◽  
Energy Levels ◽  
Scalar Potential ◽  
Scalar Particle ◽  
Klein Theory ◽  
Klein Gordon ◽  
Quantum Flux

In this paper, we study a relativistic quantum dynamics of spin-0 scalar particle interacts with scalar potential in the presence of a uniform magnetic field and quantum flux in background of Kaluza–Klein theory (KKT). We solve Klein–Gordon equation in the considered framework and analyze the relativistic analogue of the Aharonov–Bohm effect for bound states. We show that the energy levels depend on the global parameters characterizing the spacetime, scalar potential and the magnetic field which break their degeneracy.

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