On the classical dynamics of charged particle in special class of spatially non-uniform magnetic field

Singh, Ranveer Kumar

doi:10.1007/s12648-018-1316-z

Cited by 3 publications

(2 citation statements)

References 11 publications

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“…In the limits of Θ → 0 and → 0, the above result reduces to the commutative one, which corresponds to that of ref. [26] (with a little difference in "4" instead of "2". In our calculations ∝ 2 (the symmetric gauge), whereas the author of the mentioned work considered ∝ ), and it is given bȳ…”

Section: Two-dimensional Noncommutative Pauli Equationmentioning

confidence: 99%

Two-Dimensional Pauli Equation in Noncommutative Phase-Space

Haouam¹

2021

Ukr. J. Phys.

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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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Section: Two-dimensional Noncommutative Pauli Equationmentioning

confidence: 99%

Two-Dimensional Pauli Equation in Noncommutative Phase-Space

Haouam¹

2021

Ukr. J. Phys.

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“…which gives a non-uniform magnetic field in the ẑ-direction as B = B 0 e −αx ẑ, where B 0 is a constant, and the parameter α is the non-uniformity parameter [45]. This form of magnetic field can have a role in different branches of physics, like in chiral magnetic effect in particle physics [46], searching the quantum structure of graphene [47], and within the supersymmetric quantum mechanics where supersymmetry is broken [48]. In order to have also an eigenfunction of y-and z-component of the linear momentum operator, we write the wave function as…”

Section: Modelmentioning

confidence: 99%

Thermodynamic properties of a charged particle in non-uniform magnetic field

2021

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We solve the Schrödinger equation for a charged particle in the non-uniform magnetic field by using the Nikiforov-Uvarov method. We find the energy spectrum and the wave function, and present an explicit relation for the partition function. We give analytical expressions for the thermodynamic properties such as mean energy and magnetic susceptibility, and analyze the entropy, free energy and specific heat of this system numerically. It is concluded that the specific heat and magnetic susceptibility increase with external magnetic field strength and different values of the non-uniformity parameter, α, in the low temperature region, while the mentioned quantities are decreased in high temperature regions due to increasing the occupied levels at these regions. The non-uniformity parameter has the same effect with a constant value of the magnetic field on the behavior of thermodynamic properties.On the other hand, the results show that transition from positive to negative magnetic susceptibility depends on the values of non-uniformity parameter in the constant external magnetic field.

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On the Fisk–Tait equation for spin-3/2 fermions interacting with an external magnetic field in noncommutative space-time

Haouam¹

2020

J. Phys. Stud.

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The Fisk-Tait equation in interaction with an external magnetic field in noncommutative spacetime is investigated, consequently, we studied the continuity equation in both commutative and noncommutative space-time; there we examined the influence of the space-time noncommutativity on the current density quadri-vector. And we also find that the total charge obtained from the probability density still indefinite even when space does not commute. Furthermore we found the spin current density in the two different spin directions. We also investigated the linking between the fermions and the bosons in the Fock space using the Holstein-Primakoff transformation.Over the years the particle equations for an arbitrary spin was considered the subject for careful investigations, that's why today we are interested in the relativistic equations that describe the motion of spin-3/2 particles. Such as the relativistic Rarita-Schwinger equation (1940) [1], the Fisk-Tait equation (1973) [2], Hurley's field equation [3], Bhabha-Gupta equation (Bhabha, Gupta 1952, 1954, 1974, the approach for arbitrary spin equation by V. Bargman, E.P. Wigner (1948) [6]. Also the Heisenberg equations of motion for the spin-3/2 field (1977) [7], in which, it is shown for dynamical systems with constraints depending upon external fields, the Lagrange and Heisenberg equations of motion are the same for the quantized charged spin-3/2 field in the presence of a minimal external electromagnetic interaction. The Rarita-Schwinger spin-3/2 equation in the weak-field limit is obtained to satisfy the Heisenberg equations of motion. This is similar to the case of spin-3/2 field minimally coupled with an external electromagnetic field by Mainland and Sudarshan (1973) [8].As well recently, we have the link between the relativistic canonical quantum mechanics of arbitrary spin and the covariant local field theory by V.M. Simulik (2017) [9] (where the found equations are without redundant components). Where it has been confirmed that, the synthesis of the relativistic canonical quantum mechanics of the spins-3/2 particle and antiparticle doublet is completely similar to the synthesis of the Dirac equation from the relativistic canonical quantum mechanics of the spin-1/2 particle-antiparticle doublet. On the basis of the investigation of solutions and transformation properties with respect to the Poincare group the obtained new 8-component equation is suggested to be well defined for the description of spin s=3/2 fermions. Despite the Rarita-Schwinger equation which has 16 components and needs the additional condition.But the equation for a particle of spin-3/2 originally was given by Fierz and Pauli (I939) in spinor form [10]. Knowing that the Klein-Gordon, Dirac, and Proca equations provide a relativistic description of the particles that have the lowest spins cases (S=0, 1/2, 1 respectively).For instance, the Rarita-Schwinger equation was formulated for the first time by William Rarita and Julian Schwinger, it was the most famous equation that describes the m...

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On the classical dynamics of charged particle in special class of spatially non-uniform magnetic field

Cited by 3 publications

References 11 publications

Two-Dimensional Pauli Equation in Noncommutative Phase-Space

Two-Dimensional Pauli Equation in Noncommutative Phase-Space

Thermodynamic properties of a charged particle in non-uniform magnetic field

On the Fisk–Tait equation for spin-3/2 fermions interacting with an external magnetic field in noncommutative space-time

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