Landau Levels in a Gravitational Field: The Schwarzschild Spacetime Case

We investigate the gravitational effect on Landau levels. We show that the familiar infinite Landau degeneracy of the energy levels of a quantum particle moving inside a uniform and constant magnetic field is removed by the interaction of the particle with a gravitational field. Two independent approaches are used to solve the relevant Schrödinger equation within the Newtonian approximation. It is found that both approaches yield qualitatively similar results within their respective approximations. With the goal of clarifying some results found in the literature concerning the use of a third independent approach for extracting the quantization condition based on a similar differential equation, we show that such an approach cannot yield a general and yet consistent result. We point out to the more accurate, but impractical, way to use such an approach; a way which does in principle yield a consistent quantization condition. We discuss how our results could be used to contribute in a novel way to the existing methods for testing gravity at the tabletop experiments level as well as at the astrophysical observational level by deriving the corrections brought by Yukawa-like and power-law deviations from the inverse-square law. The full relativistic regime is also examined in detail.

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Spin-1/2 Particles under the Influence of a Uniform Magnetic Field in the Interior Schwarzschild Solution

Universe ◽

10.3390/universe7120467 ◽

2021 ◽

Vol 7 (12) ◽

pp. 467

Author(s):

Fayçal Hammad ◽

Alexandre Landry ◽

Parvaneh Sadeghi

Keyword(s):

Magnetic Field ◽

Magnetic Fields ◽

Total Mass ◽

Uniform Magnetic Field ◽

Energy Levels ◽

Relativistic Wave Equation ◽

Relativistic Wave ◽

Schwarzschild Solution ◽

Relativistic Regime ◽

The Magnetic Field

The relativistic wave equation for spin-1/2 particles in the interior Schwarzschild solution in the presence of a uniform magnetic field is obtained. The fully relativistic regime is considered, and the energy levels occupied by the particles are derived as functions of the magnetic field, the radius of the massive sphere and the total mass of the latter. As no assumption is made on the relative strengths of the particles’ interaction with the gravitational and magnetic fields, the relevance of our results to the physics of the interior of neutron stars, where both the gravitational and the magnetic fields are very intense, is discussed.

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Asymptotic behavior of the energy levels of a quantum particle in a homogeneous magnetic field, perturbed by a decreasing electric field. I

Journal of Soviet Mathematics ◽

10.1007/bf01104868 ◽

1986 ◽

Vol 35 (1) ◽

pp. 2201-2212 ◽

Cited By ~ 12

Author(s):

A. V. Sobolev

Keyword(s):

Magnetic Field ◽

Asymptotic Behavior ◽

Electric Field ◽

Quantum Particle ◽

Energy Levels ◽

Homogeneous Magnetic Field

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Relativistic Landau quantization in non-uniform magnetic field and its applications to white dwarfs and quantum information

SciPost Physics ◽

10.21468/scipostphys.11.5.093 ◽

2021 ◽

Vol 11 (5) ◽

Author(s):

Srishty Aggarwal ◽

Banibrata Mukhopadhyay ◽

Gianluca Gregori

Keyword(s):

Magnetic Field ◽

Angular Momentum ◽

Quantum Information ◽

Magnetic Fields ◽

White Dwarfs ◽

Energy Levels ◽

Landau Levels ◽

Constant Field ◽

Angular Momenta ◽

Spatially Varying

We investigate the two-dimensional motion of relativistic cold electrons in the presence of `strictly’ spatially varying magnetic fields satisfying, however, no magnetic monopole condition. We find that the degeneracy of Landau levels, which arises in the case of the constant magnetic field, lifts out when the field is variable and the energy levels of spin-up and spin-down electrons align in an interesting way depending on the nature of change of field. Also, the varying magnetic field splits Landau levels of electrons with zero angular momentum from positive angular momentum, unlike the constant field which only can split the levels between positive and negative angular momenta. Exploring Landau quantization in non-uniform magnetic fields is a unique venture on its own and has interdisciplinary implications in the fields ranging from condensed matter to astrophysics to quantum information. As examples, we show magnetized white dwarfs, with varying magnetic fields, involved simultaneously with Lorentz force and Landau quantization affecting the underlying degenerate electron gas, exhibiting a significant violation of the Chandrasekhar mass-limit; and an increase in quantum speed of electrons in the presence of a spatially growing magnetic field.

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Magnetization of disclinated graphene in nonuniform magnetic field

International Journal of Modern Physics B ◽

10.1142/s0217979217500138 ◽

2017 ◽

Vol 31 (04) ◽

pp. 1750013 ◽

Cited By ~ 1

Author(s):

M. Roshanzamir-Nikou ◽

H. Goudarzi

Keyword(s):

Magnetic Field ◽

Topological Defect ◽

Energy Levels ◽

Persistent Current ◽

Landau Levels ◽

Nonuniform Magnetic Field ◽

Explicit Dependence ◽

Curved Space ◽

Aharonov Bohm ◽

Physical Quantities

Two-dimensional disclinated atomic graphene layer in curved space–time is exactly discussed, and the explicit dependence of Landau levels on the topological defect and external magnetic field are obtained in the presence of nonuniform magnetic field. It is worth mentioning that the presence of topological defect reduces the degeneracy of energy levels. The persistent current, magnetization, susceptibility and the magnetoresistance of structure are investigated. It can be shown that the curvature of the conical surface affects the pattern of oscillations of persistent current and, of course, corresponding magnetoresistance. The behavior of the above physical quantities as a function of magnetic flux is explicitly found for various defects. We observe that increasing magnetic field leads to a aperiodic oscillation. The large Aharonov–Bohm flux gives rise to vanish the magnetization oscillations.

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Dynamical and structural symmetries for the highest Landau levels on the AdS 2

Open Physics ◽

10.2478/s11534-011-0113-5 ◽

2012 ◽

Vol 10 (2) ◽

Author(s):

Pakhshan Espoukeh ◽

Hossein Fakhri

Keyword(s):

Magnetic Field ◽

Differential Operators ◽

Dynamical Symmetry ◽

Quantization Condition ◽

Landau Levels ◽

Irreducible Representations ◽

Legendre Functions ◽

Ladder Operators ◽

Associated Legendre Functions ◽

Dirac Quantization

AbstractThe aim of the paper is to use the recurrence relations with respect to both indices of the associated Legendre functions for the extraction of the Dirac quantization condition and dynamical symmetry group U(1, 1) corresponding to the highest Landau levels on the hyperbolic plane with uniform magnetic field B. Irreducible representations of the su(2) algebra are obtained by the ladder differential operators which change B by 1/2 unit and mode number by one unit. Two different classes of the irreducible representations of SU(1, 1) with the even and odd boson numbers 2B − 1/2 are extracted for the Bargmann indices 1/4 and 3/4, respectively. Finally, we show that shape invariance symmetry is realized by the ladder operators which shift only the magnetic field B by 1/2 unit.

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MATHEMATICAL MODELING OF TEMPERATURE EFFECT ON THE FAN CHART OF MAGNETOABSORPTION SPECTRUM IN SEMICONDUCTORS

Alternative Energy and Ecology (ISJAEE) ◽

10.15518/isjaee.2019.01-03.104-115 ◽

2019 ◽

pp. 104-115

Author(s):

G. Gulyamov ◽

U. I. Erkaboev ◽

A. G. Gulyamov

Keyword(s):

Mathematical Modeling ◽

Magnetic Field ◽

Temperature Dependence ◽

Density Of States ◽

Landau Levels ◽

Joint Density ◽

Narrow Gap ◽

Narrow Gap Semiconductors ◽

Dispersion Law ◽

The Magnetic Field

The article considers the oscillations of interband magneto-optical absorption in semiconductors with the Kane dispersion law. We have compared the changes in oscillations of the joint density of states with respect to the photon energy for different Landau levels in parabolic and non-parabolic zones. An analytical expression is obtained for the oscillation of the combined density of states in narrow-gap semiconductors. We have calculated the dependence of the maximum photon energy on the magnetic field at different temperatures. A theoretical study of the band structure showed that the magnetoabsorption oscillations decrease with an increase in temperature, and the photon energies nonlinearly depend on a strong magnetic field. The article proposes a simple method for calculating the oscillation of joint density of states in a quantizing magnetic field with the non-quadratic dispersion law. The temperature dependence of the oscillations joint density of states in semiconductors with non-parabolic dispersion law is obtained. Moreover, the article studies the temperature dependence of the band gap in a strong magnetic field with the non-quadratic dispersion law. The method is applied to the research of the magnetic absorption in narrow-gap semiconductors with nonparabolic dispersion law. It is shown that as the temperature increases, Landau levels are washed away due to thermal broadening and density of states turns into a density of states without a magnetic field. Using the mathematical model, the temperature dependence of the density distribution of energy states in strong magnetic fields is considered. It is shown that the continuous spectrum of the density of states, measured at the temperature of liquid nitrogen, at low temperatures turns into discrete Landau levels. Mathematical modeling of processes using experimental values of the continuous spectrum of the density of states makes it possible to calculate discrete Landau levels. We have created the three-dimensional fan chart of magneto optical oscillations of semiconductors with considering for the joint density of energy states. For a nonquadratic dispersion law, the maximum frequency of the absorbed light and the width of the forbidden band are shown to depend nonlinearly on the magnetic field. Modeling the temperature dependence allowed us to determine the Landau levels in semiconductors in a wide temperature spectrum. Using the proposed model, the experimental results obtained for narrow-gap semiconductors are analyzed. The theoretical results are compared with experimental results.

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Combined Effect of Magnetic Field and Lateral Mass Transfer on Non-Darsy Axisymmetric Free Convection in a Power-Law Fluid Saturated Porous Medium

Journal of Porous Media ◽

10.1615/jpormedia.v7.i1.70 ◽

2004 ◽

Vol 7 (1) ◽

pp. 65-71 ◽

Cited By ~ 3

Author(s):

M. F. El-Amin ◽

M. A. El-Hakiem ◽

M. A. Mansour

Keyword(s):

Magnetic Field ◽

Mass Transfer ◽

Porous Medium ◽

Free Convection ◽

Power Law ◽

Saturated Porous Medium ◽

Combined Effect ◽

Lateral Mass ◽

Power Law Fluid ◽

Fluid Saturated Porous Medium

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Jet Impingement Heat Transfer of Confined Single and Double Jets with Non-Newtonian Power Law Nanofluid under the Inclined Magnetic Field Effects for a Partly Curved Heated Wall

Sustainability ◽

10.3390/su13095086 ◽

2021 ◽

Vol 13 (9) ◽

pp. 5086

Author(s):

Fatih Selimefendigil ◽

Hakan F. Oztop ◽

Ali J. Chamkha

Keyword(s):

Magnetic Field ◽

Heat Transfer ◽

Particle Size ◽

Aspect Ratio ◽

Power Law ◽

Volume Fraction ◽

Inclined Magnetic Field ◽

Magnetic Field Effects ◽

Power Law Nanofluid ◽

Power Law Index

Single and double impinging jets heat transfer of non-Newtonian power law nanofluid on a partly curved surface under the inclined magnetic field effects is analyzed with finite element method. The numerical work is performed for various values of Reynolds number (Re, between 100 and 300), Hartmann number (Ha, between 0 and 10), magnetic field inclination (γ, between 0 and 90), curved wall aspect ratio (AR, between 01. and 1.2), power law index (n, between 0.8 and 1.2), nanoparticle volume fraction (ϕ, between 0 and 0.04) and particle size in nm (dp, between 20 and 80). The amount of rise in average Nusselt (Nu) number with Re number depends upon the power law index while the discrepancy between the Newtonian fluid case becomes higher with higher values of power law indices. As compared to case with n = 1, discrepancy in the average Nu number are obtained as −38% and 71.5% for cases with n = 0.8 and n = 1.2. The magnetic field strength and inclination can be used to control the size and number or vortices. As magnetic field is imposed at the higher strength, the average Nu reduces by about 26.6% and 7.5% for single and double jets with n greater than 1 while it increases by about 4.78% and 12.58% with n less than 1. The inclination of magnetic field also plays an important role on the amount of enhancement in the average Nu number for different n values. The aspect ratio of the curved wall affects the flow field slightly while the average Nu variation becomes 5%. Average Nu number increases with higher solid particle volume fraction and with smaller particle size. At the highest particle size, it is increased by about 14%. There is 7% variation in the average Nu number when cases with lowest and highest particle size are compared. Finally, convective heat transfer performance modeling with four inputs and one output is successfully obtained by using Adaptive Neuro-Fuzzy Interface System (ANFIS) which provides fast and accurate prediction results.

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