Infinite degeneracy of Landau levels from the Euclidean symmetry with central extension revisited

Murgan, Rajan

doi:10.1088/1361-6404/abdf35

Cited by 2 publications

(3 citation statements)

References 12 publications

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“…We also want to inspect the Hamiltonian parameters in the corresponding commutative space. We see from equations (7), ( 8), (9), the time dependent Hamiltonian coefficients in the commutative situation has the following form,…”

Section: Study Of the Corresponding Eigenfunctionsmentioning

confidence: 99%

“…Excited coherent states for a charged particle in a uniform magnetic field were introduced in [6]. Very recently, the Landau problem has been revisited in a pedagogical way in [7], also the Lie transformation method has been employed in [8] to determine the time-evolution of the quantum state of a parametric oscillator. In addition, one may also consider an electric field lying along the plane of oscillation.…”

Section: Introductionmentioning

confidence: 99%

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Investigation of a harmonic oscillator in a magnetic field with damping and time dependent noncommutativity

Dutta¹,

Ganguly²,

Gangopadhyay³

2021

Phys. Scr.

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This work is devoted to find the eigenstates of a two dimensional damped harmonic oscillator in the presence of an external magnetic field varying with respect to time with a time dependent spatial noncommutativity. It is observed that there are some specific choices of the damping factor, the time dependent frequency of the oscillator and the time dependent external magnetic field for which one can obtain interesting solutions of the time dependent noncommutative parameters. These solutions follow from the non-linear Ermakov-Pinney equation. We then obtain exact analytic forms for the phase which relates the eigenstates of the Hamiltonian with the eigenstates of the Lewis invariant. An important aspect of this study is to see the relationship between the damping and the applied magnetic field on the energy profile of the system. For this we compute the expectation value of the Hamiltonian. These are found to vary with time for different solutions of the Ermakov-Pinney equation corresponding to different choices of the damping factor, the time dependent frequency of the oscillator and the time dependent applied magnetic field. Finally, we compare our results with those in the absence of the magnetic field to determine the effect of the applied field on our system.

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Section: Study Of the Corresponding Eigenfunctionsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Investigation of a harmonic oscillator in a magnetic field with damping and time dependent noncommutativity

Dutta¹,

Ganguly²,

Gangopadhyay³

2021

Phys. Scr.

View full text Add to dashboard Cite

show abstract

“…where, 𝑝̂ is the momentum operator and 𝐴 is the vector potential related to the B introduced in the z-direction. By choosing a gauge such as, 𝐴 = 𝐵 𝑧 𝑥𝑦 ̂ , the wave function takes the following form [15,17]:…”

Section: The Energymentioning

confidence: 99%

Temperature and magnetic field effect on the thermodynamic properties of 2DEG

Bouzgarrou

Almutairi

2023

Preprint

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A numerical calculation of the temperature and magnetic field dependence of the specific heat capacity, the magnetization, and the chemical potential is carried out. Of particular interest are the properties of the energy of a magnetic field in a two-dimensional electron gas exposed to a magnetic field. Thus, in this paper, we illustrate the effect of temperature on the oscillation dHvA of specific heat capacity and magnetization. As well a mathematical model has been developed for calculating the temperature dependence of the oscillations of the chemical potential and the density of states under the influence of a magnetic field. Using the proposed model, the results were explained at different broadening factors Γ. The calculated results show that specific heat capacity and magnetization increase as the magnetic field increases. Additionally, these increases carry out that the magnetic field is large enough to neglect the mixing of Landau levels caused by the sharp peak of Landeau levels. Moreover, the 2D dHvA effect is characterized by a sawtooth strap at a very low temperature.

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Infinite degeneracy of Landau levels from the Euclidean symmetry with central extension revisited

Cited by 2 publications

References 12 publications

Investigation of a harmonic oscillator in a magnetic field with damping and time dependent noncommutativity

Investigation of a harmonic oscillator in a magnetic field with damping and time dependent noncommutativity

Temperature and magnetic field effect on the thermodynamic properties of 2DEG

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