Landau problem with time dependent mass in time dependent electric and harmonic background fields

Lawson, Latévi M.; Avossevou, Gabriel Y. H.

doi:10.1063/1.5001174

Cited by 10 publications

(21 citation statements)

References 45 publications

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“…In addition, one may also consider an electric field lying along the plane of oscillation. The eigenfunction and the eigenvalues of a charged particle in a magnetic field in the presence of a time-dependent background electric field with time-dependent mass and frequency have been determined in [1]. The problem becomes even more fascinating when one places the Landau oscillator in a noncommutative phase space.…”

Section: Introductionmentioning

confidence: 99%

Exact Solutions of a Damped Harmonic Oscillator in a Time Dependent Noncommutative Space

2020

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In this paper we have obtained the exact eigenstates of a two dimensional damped harmonic oscillator in the presence of an external magnetic field varying with respect to time in time dependent noncommutative space. It has been observed that for some specific choices of the damping factor, the time dependent frequency of the oscillator and the time dependent external magnetic field, there exists interesting solutions of the time dependent noncommutative parameters following from the solutions of the Ermakov-Pinney equation. Further, these solutions enable us to get exact analytic forms for the phase which relates the eigenstates of the Hamiltonian with the eigenstates of the Lewis invariant. Then we compute the expectation value of the Hamiltonian.The expectation values of the energy 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. We also compare our results with those in the absence of the magnetic field obtained earlier.

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Section: Introductionmentioning

confidence: 99%

Exact Solutions of a Damped Harmonic Oscillator in a Time Dependent Noncommutative Space

2020

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“…Recently, the mathematical and statistical properties of PACSs are studied for the SU (2) coherent states [22,37]. We extend these results into our recently model studied in [1] namely the time-dependent Landau problem (TDLP). To do so, we organise the paper as follows.…”

Section: Introductionmentioning

confidence: 74%

Photon-added BarutGirardello like coherent states of time-dependent Landau problem

Lawson¹,

Sodoga²,

Avossevou³

2021

Preprint

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Recently, we have determined the spectrum and the wave functions of the Hamiltonian of a Landau particle with time-dependent mass and frequency undergoing the influence of a uniform time-dependent electric field [J. Math. Phys. 56, 072104 (2018)]. In the present paper we extend the study of this model that we name the time-dependent Landau problem into the context of coherent states. By means of the traditional factorization method of the eigenfunctions of this system expressed in terms of the generalized Laguerre polynomials, we derive the generators of the su(1, 1) Lie algebra and we construct the coherent states à la Barut-Girardello. These states are shown to satisfy the Klauder's mathematical requirement to build coherent states and some of their statistical properties are calculated and analyzed. We find that these states are sub-Poissonian in nature. We show that, addition of photons from these coherent states, increases the statistical properties and changes the mathematical properties of these states.

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“…The damped harmonic oscillator is one of the most fascinating systems that have remained over the years a constant source of inspiration in quantum physics [14,15]. It has attracted much attention in the literature [16,17,18,19,20,21] since the problem related to this system is far from having a satisfactory solution. In fact the quantization of dissipative systems well known in the literature as Caldirola and Kanai system [14,15] has been criticized for violating certain laws of quantum theory.…”

Section: Damped Harmonic Oscillator In Sds Spacementioning

confidence: 99%

“…The solutions are periodic, but not sinusoidal, and the frequency now depends on the energy of the oscillator. In the limit α → 0, one recovers the flat Snyder oscillator [10] Returning to the original variables x(t) and p(t) of the Hamiltonian (18) and with the help of the relation (21) we have:…”

Section: Damped Harmonic Oscillator In Sds Spacementioning

confidence: 99%

The damped harmonic oscillator at the classical limit of the Snyder-de Sitter space

Lawson,

Nonkané,

Sodoga

2021

Preprint

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Valtancoli has shown how the deformation of the canonical transformations can be made compatible with the deformed Poisson brackets [J. Math. Phys. 56, 122107 (2015)]. Based on this work and through an appropriate canonical transformation, we solve the problem of one dimensional (1D) damped harmonic oscillator at the classical limit of the Snyder-de Sitter (SdS) space. We show that the equations of the motion can be described by trigonometric functions with frequency and period depending on the deformed and the damped parameters. We eventually discuss about the influences of these parameters on the motion of the system.

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Landau problem with time dependent mass in time dependent electric and harmonic background fields

Cited by 10 publications

References 45 publications

Exact Solutions of a Damped Harmonic Oscillator in a Time Dependent Noncommutative Space

Exact Solutions of a Damped Harmonic Oscillator in a Time Dependent Noncommutative Space

Photon-added BarutGirardello like coherent states of time-dependent Landau problem

The damped harmonic oscillator at the classical limit of the Snyder-de Sitter space

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