INFLUENCE OF THE GRAVITATIONAL FIELD ON THE QUANTUM STATES OF THE ELECTRON IN A PENNING TRAP

1996 ◽  
Vol 11 (17) ◽  
pp. 1429-1443
Author(s):  
R. STAUDT ◽  
U.E. SCHRÖDER
Keyword(s):  
Electromagnetic Field ◽  
Gravitational Field ◽  
Dirac Equation ◽  
Penning Trap ◽  
Energy Levels ◽  
Quantum States ◽  
Minimal Coupling ◽  
Relative Shift ◽  
The Earth ◽  
Resulting Effect

Starting from the general covariant Dirac equation with minimal coupling of an electromagnetic field the corrections to the energy levels of the electron in a Penning trap caused by the gravitational field of the Earth are computed. Our discussion shows that the resulting effect is detectable only at the specific eigenfrequencies of the electron. The relative shift of these frequencies due to the gravitational field is found to be 2.1×10–9. It is briefly indicated how this effect in principle could be observed in suitable experiments performed with higher precision.

scholarly journals The Dirac Electron Consistent with Proper Gravitational and Electromagnetic Field of the Kerr–Newman Solution

Galaxies ◽  
2021 ◽  
Vol 9 (1) ◽  
pp. 18
Author(s):  
Alexander Burinskii
Keyword(s):  
Electromagnetic Field ◽  
Quantum Theory ◽  
Gravitational Field ◽  
Dirac Equation ◽  
Higgs Field ◽  
Vacuum State ◽  
Relativistic String ◽  
Dirac Equations ◽  
Dirac Electron ◽  
Relativistic Scattering

The Dirac electron is considered as a particle-like solution consistent with its own Kerr–Newman (KN) gravitational field. In our previous works we considered the regularized by López KN solution as a bag-like soliton model formed from the Higgs field in a supersymmetric vacuum state. This bag takes the shape of a thin superconducting disk coupled with circular string placed along its perimeter. Using the unique features of the Kerr–Schild coordinate system, which linearizes Dirac equation in KN space, we obtain the solution of the Dirac equations consistent with the KN gravitational and electromagnetic field, and show that the corresponding solution takes the form of a massless relativistic string. Obvious parallelism with Heisenberg and Schrödinger pictures of quantum theory explains remarkable features of the electron in its interaction with gravity and in the relativistic scattering processes.

scholarly journals Quantum states of an electromagnetic field interacting with a classical current and their applications to radiation problems

2020 ◽  
Vol 27 (4) ◽  
pp. 902-911
Author(s):  
V. G. Bagrov ◽  
D. M. Gitman ◽  
A. A. Shishmarev ◽  
A. J. D. Farias
Keyword(s):  
Electromagnetic Field ◽  
Synchrotron Radiation ◽  
Dirac Equation ◽  
Photon Emission ◽  
Quantum States ◽  
Photon Radiation ◽  
Electric Currents ◽  
Scalar Particles ◽  
Two Photon ◽  
The Relationship

Synchrotron radiation was originally studied by classical methods using the Liénard–Wiechert potentials of electric currents. Subsequently, quantum corrections to the classical formulas were studied, considering the emission of photons arising from electronic transitions between spectral levels, described in terms of the Dirac equation. In this paper, an intermediate approach is considered, in which electric currents generating the radiation are considered classically while the quantum nature of the radiation is taken into account exactly. Such an approximate approach may be helpful in some cases; it allows one to study one-photon and multi-photon radiation without complicating calculations using corresponding solutions of the Dirac equation. Here, exact quantum states of an electromagnetic field interacting with classical currents are constructed and their properties studied. With their help, the probability of photon emission by classical currents is calculated and relatively simple formulas for one-photon and multi-photon radiation are obtained. Using the specific circular electric current, the corresponding synchrotron radiation is calculated. The relationship between the obtained results and those known before are discussed, for example with the Schott formula, with Schwinger calculations, with one-photon radiation of scalar particles due to transitions between Landau levels, and with some previous results of calculating two-photon synchrotron radiation.

scholarly journals Is gravitational mass of a composite quantum body equivalent to its energy?

Open Physics ◽  
2013 ◽  
Vol 11 (8) ◽  
Author(s):  
Andrei Lebed
Keyword(s):  
Gravitational Field ◽  
Mass Operator ◽  
Energy Operator ◽  
Microscopic Level ◽  
Quantum States ◽  
Gravitational Mass ◽  
Expectation Values ◽  
The Earth ◽  
Stationary Quantum ◽  
Passive Gravitational Mass

AbstractWe define passive gravitational mass operator of a hydrogen atom in the post-Newtonian approximation of general relativity and show that it does not commute with energy operator, taken in the absence of gravitational field. Nevertheless, the equivalence between the expectation values of passive gravitational mass and energy is shown to survive for stationary quantum states. Inequivalence between passive gravitational mass and energy at a macroscopic level results in time dependent oscillations of the expectation values of passive gravitational mass for superpositions of stationary quantum states, where the equivalence restores after averaging over time. Inequivalence between gravitational mass and energy at a microscopic level reveals itself as unusual electromagnetic radiation, emitted by the atoms, supported and moved in the Earth gravitational field with constant velocity using spacecraft or satellite, which can be experimentally measured.

scholarly journals THE SCHRÖDINGER PICTURE OF THE DIRAC QUANTUM MECHANICS ON SPATIALLY FLAT ROBERTSON–WALKER BACKGROUNDS

2007 ◽  
Vol 22 (39) ◽  
pp. 2965-2969 ◽  
Author(s):  
ION I. COTĂESCU
Keyword(s):  
Quantum Mechanics ◽  
Gravitational Field ◽  
Dirac Equation ◽  
Time Evolution ◽  
Hamiltonian Operator ◽  
De Sitter ◽  
Minimal Coupling ◽  
Cartesian Coordinates ◽  
Schrödinger Picture

The time evolution Schrödinger picture of the Dirac quantum mechanics is defined in charts with spatially flat Robertson–Walker metrics and Cartesian coordinates. The main observables of this picture are identified, including the interacting part of the Hamiltonian operator produced by the minimal coupling with the gravitational field. It is shown that in this approach new Dirac quantum modes on de Sitter spacetimes may be found analytically solving the Dirac equation.

The analysis is geometrically stable orbits of spacecraft remote sensing of the Еarth

2018 ◽  
Vol 15 (1) ◽  
pp. 12-22
Author(s):  
V. M. Artyushenko ◽  
D. Y. Vinogradov
Keyword(s):  
Remote Sensing ◽  
Gravitational Field ◽  
State Vector ◽  
Semimajor Axis ◽  
The State ◽  
Zonal Harmonics ◽  
The Earth ◽  
Conditions Of Stability

The article reviewed and analyzed the class of geometrically stable orbits (GUO). The conditions of stability in the model of the geopotential, taking into account the zonal harmonics. The sequence of calculation of the state vector of GUO in the osculating value of the argument of the latitude with the famous Ascoli-royski longitude of the ascending node, inclination and semimajor axis. The simulation is obtained the altitude profiles of SEE regarding the all-earth ellipsoid model of the gravitational field of the Earth given 7 and 32 zonal harmonics.

Spheric radial basis functions in Mahalanobis measuring for displaying local field features

2019 ◽  
Vol 952 (10) ◽  
pp. 2-9
Author(s):  
Yu.M. Neiman ◽  
L.S. Sugaipova ◽  
V.V. Popadyev
Keyword(s):  
Gravitational Field ◽  
Quadratic Form ◽  
Local Field ◽  
Euclidean Distance ◽  
Basis Functions ◽  
Spherical Functions ◽  
Local Models ◽  
Stationary Field ◽  
Modeling Process ◽  
The Earth

As we know the spherical functions are traditionally used in geodesy for modeling the gravitational field of the Earth. But the gravitational field is not stationary either in space or in time (but the latter is beyond the scope of this article) and can change quite strongly in various directions. By its nature, the spherical functions do not fully display the local features of the field. With this in mind it is advisable to use spatially localized basis functions. So it is convenient to divide the region under consideration into segments with a nearly stationary field. The complexity of the field in each segment can be characterized by means of an anisotropic matrix resulting from the covariance analysis of the field. If we approach the modeling in this way there can arise a problem of poor coherence of local models on segments’ borders. To solve the above mentioned problem it is proposed in this article to use new basis functions with Mahalanobis metric instead of the usual Euclidean distance. The Mahalanobis metric and the quadratic form generalizing this metric enables us to take into account the structure of the field when determining the distance between the points and to make the modeling process continuous.

scholarly journals NONCOMMUTATIVE GRAPHENE

2013 ◽  
Vol 28 (16) ◽  
pp. 1350064 ◽  
Author(s):  
CATARINA BASTOS ◽  
ORFEU BERTOLAMI ◽  
NUNO COSTA DIAS ◽  
JOÃO NUNO PRATA
Keyword(s):  
Magnetic Field ◽  
External Magnetic Field ◽  
Dirac Equation ◽  
Energy Levels ◽  
Dirac Fermions ◽  
Two Dimensional ◽  
Dirac System ◽  
Noncommutative Parameter

We consider a noncommutative description of graphene. This description consists of a Dirac equation for massless Dirac fermions plus noncommutative corrections, which are treated in the presence of an external magnetic field. We argue that, being a two-dimensional Dirac system, graphene is particularly interesting to test noncommutativity. We find that momentum noncommutativity affects the energy levels of graphene and we obtain a bound for the momentum noncommutative parameter.

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