The quantization condition in the presence of a magnetic field and quasiclassical eigenvalues of the Kepler problem with a centrifugal potential and Dirac’s monopole field

1990 ◽  
Vol 31 (6) ◽  
pp. 1388-1394 ◽  
Author(s):  
Akira Yoshioka ◽  
Kiyotaka Ii
Keyword(s):  
Magnetic Field ◽  
Kepler Problem ◽  
Quantization Condition

scholarly journals DYNAMICAL (SUPER)SYMMETRIES OF MONOPOLES AND VORTICES

2006 ◽  
Vol 18 (03) ◽  
pp. 329-347 ◽  
Author(s):  
P. A. HORVÁTHY
Keyword(s):  
Magnetic Field ◽  
Static Magnetic Field ◽  
Kepler Problem ◽  
Dynamical Symmetry ◽  
Magnetic Vortex ◽  
Supersymmetry Algebra ◽  
Dirac Monopole ◽  
The One ◽  
Kaluza Klein

The dynamical (super)symmetries for various monopole systems are reviewed. For a Dirac monopole, non-smooth Runge–Lenz vector can exist; there is, however, a spectrum-generating conformal o(2,1) dynamical symmetry that extends into osp(1/1) or osp(1/2) for spin 1/2 particles. Self-dual 't Hooft–Polyakov-type monopoles admit an su(2/2) dynamical supersymmetry algebra, which allows us to reduce the fluctuation equation to the spin 0 case. For large r, the system reduces to a Dirac monopole plus a suitable inverse-square potential considered before by McIntosh and Cisneros, and by Zwanziger in the spin 0 case, and to the "dyon" of D'Hoker and Vinet for spin 1/2. The asymptotic system admits a Kepler-type dynamical symmetry as well as a "helicity-supersymmetry" analogous to the one Biedenharn found in the relativistic Kepler problem. Similar results hold for the Kaluza–Klein monopole of Gross–Perry–Sorkin. For the magnetic vortex, the N = 2 supersymmetry of the Pauli Hamiltonian in a static magnetic field in the plane combines with the o(2) × o(2,1) bosonic symmetry into an o(2) × osp(1/2) dynamical superalgebra.

scholarly journals nanoSQUID operation using kinetic rather than magnetic induction

2016 ◽  
Vol 6 (1) ◽  
Author(s):  
Adam N. McCaughan ◽  
Qingyuan Zhao ◽  
Karl K. Berggren
Keyword(s):  
Magnetic Field ◽  
Thin Films ◽  
Applied Magnetic Field ◽  
Magnetic Induction ◽  
Quantization Condition ◽  
Kinetic Inductance ◽  
Superconducting Thin Films ◽  
Magnetic Inductance ◽  
Measurement Results ◽  
Superconducting Loop

Abstract We report on a method of nanoSQUID modulation which uses kinetic inductance rather than magnetic inductance to manip-ulate the internal fluxoid state. We produced modulation using injected current rather than an applied magnetic field. Using this injected current, we were able to observe the triangle-wave shaped modulation of the device critical current which was periodic according to the London fluxoid quantization condition. The measurement results also confirmed that the fluxoid state inside a superconducting loop can be manipulated using primarily kinetic inductance. By using primarily kinetic inductance rather than magnetic inductance, the size of the coupling inductor was reduced by a factor of 10. As a result, this approach may provide a means to reduce the size of SQUID-based superconducting electronics. Additionally, this method provides a convenient way to perform kinetic inductance characterizations of superconducting thin films.

scholarly journals CHAOS, FRACTALS AND QUANTUM POINCARÉ RECURRENCES IN DIAMAGNETIC KEPLER PROBLEM

2007 ◽  
Vol 21 (02n03) ◽  
pp. 79-96 ◽  
Author(s):  
A. UGULAVA ◽  
L. CHOTORLISHVILI ◽  
T. KERESELIDZE ◽  
V. SKRINNIKOV
Keyword(s):  
Magnetic Field ◽  
Hilbert Space ◽  
Hydrogen Atom ◽  
Strong Magnetic Field ◽  
Quantum Chaos ◽  
Kepler Problem ◽  
Quantum Mechanical ◽  
Mechanical State ◽  
Classical Chaos ◽  
Good Agreement

The statistics of quantum Poincaré recurrences in Hilbert space for diamagnetic hydrogen atom in strong magnetic field has been investigated. It has been shown that quantities characterizing classical chaos are in good agreement with the ones that are used to describe quantum chaos. The equality of classical and quantum Poincaré recurrences has been shown. It has been proved that one of the signs of the emergence of quantum chaos is the irreversible transition from a pure quantum mechanical state to a mixed one.

scholarly journals Square Roots of Kepler Ellipses, Electrons and Rydberg Atoms in a Magnetic Field

2020 ◽  
Vol 65 (10) ◽  
pp. 835
Author(s):  
Yu. P. Stepanovsky
Keyword(s):  
Magnetic Field ◽  
Solar System ◽  
Radio Telescope ◽  
Rydberg Atoms ◽  
Kepler Problem ◽  
Energy Spectra ◽  
Square Root ◽  
Hydrogen Atoms ◽  
Eccentric Anomaly ◽  
Square Roots

Young Kepler’s daring ideas on the structure of the Solar system are applied to the analysis of planetary distances in the exoplanetary system HD 10180. Using Zhukovsky’s transformation, the essence of the spinor regularization of Kepler’s problem is explained as extracting the square root of an ellipse and using a Kepler eccentric anomaly instead of the usual time. The achievements of Kharkiv radio astronomers in the search for radio recombination lines of Rydberg carbon atoms at the UTR-2 radio telescope are considered. A generalized spinor regularization of the Kepler problem is used to analyze the energy spectra of Rydberg hydrogen atoms in a magnetic field.

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

Open Physics ◽  
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.

scholarly journals Landau Levels in a Gravitational Field: The Schwarzschild Spacetime Case

Universe ◽  
2021 ◽  
Vol 7 (5) ◽  
pp. 144
Author(s):  
Alexandre Landry ◽  
Fayçal Hammad
Keyword(s):  
Magnetic Field ◽  
Differential Equation ◽  
Gravitational Field ◽  
Power Law ◽  
Quantum Particle ◽  
Energy Levels ◽  
Gravitational Effect ◽  
Quantization Condition ◽  
Landau Levels ◽  
Relativistic Regime

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.

Magnetic-field strengths from optical polarization data

1967 ◽  
Vol 31 ◽  
pp. 381-383
Author(s):  
J. M. Greenberg
Keyword(s):  
Magnetic Field ◽  
Optical Polarization ◽  
Polarization Data ◽  
Term Model ◽  
Source Of Information ◽  
Field Strengths

Van de Hulst (Paper 64, Table 1) has marked optical polarization as a questionable or marginal source of information concerning magnetic field strengths. Rather than arguing about this–I should rate this method asq+-, or quarrelling about the term ‘model-sensitive results’, I wish to stress the historical point that as recently as two years ago there were still some who questioned that optical polarization was definitely due to magnetically-oriented interstellar particles.

Observing the galactic magnetic field

1967 ◽  
Vol 31 ◽  
pp. 375-380
Author(s):  
H. C. van de Hulst
Keyword(s):  
Magnetic Field ◽  
Fair Agreement ◽  
Solar Neighbourhood ◽  
Galactic Magnetic Field ◽  
The Magnetic Field

Various methods of observing the galactic magnetic field are reviewed, and their results summarized. There is fair agreement about the direction of the magnetic field in the solar neighbourhood:l= 50° to 80°; the strength of the field in the disk is of the order of 10-5gauss.

Structure in the radiation of the galactic disk

1967 ◽  
Vol 31 ◽  
pp. 355-356
Author(s):  
R. D. Davies
Keyword(s):  
Magnetic Field ◽  
Galactic Disk ◽  
Galactic Magnetic Field ◽  
Measured Polarization

Observations at various frequencies between 136 and 1400 MHz indicate a considerable amount of structure in the galactic disk. This result appears consistent both with measured polarization percentages and with considerations of the strength of the galactic magnetic field.

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