scholarly journals Saturation of Energy Levels of the Hydrogen Atom in Strong Magnetic Field

Universe ◽  
2020 ◽  
Vol 6 (11) ◽  
pp. 204
Author(s):  
Tiago C. Adorno ◽  
Dmitry M. Gitman ◽  
Anatoly E. Shabad
Keyword(s):  
Magnetic Field ◽  
Hydrogen Atom ◽  
Effective Potential ◽  
Energy Levels ◽  
Distance Curve ◽  
Lowest Landau Level ◽  
Diagonal Approximation ◽  
The One ◽  
Limiting Values ◽  
The Magnetic Field

We demonstrate that the finiteness of the limiting values of the lower energy levels of a hydrogen atom under an unrestricted growth of the magnetic field, into which this atom is embedded, is achieved already when the vacuum polarization (VP) is calculated in the magnetic field within the approximation of the local action of Euler–Heisenberg. We find that the mechanism for this saturation is different from the one acting, when VP is calculated via the Feynman diagram in the Furry picture. We study the effective potential that appears when the adiabatic (diagonal) approximation is exploited for solving the Schrödinger equation for the longitudinal degree of freedom of the electron on the lowest Landau level in the atom. We find that the (effective) potential of a point-like charge remains nonsingular thanks to the growing screening provided by VP. The regularizing length turns out to be α/3π¯λC, where ¯λC is the electron Compton length. The family of effective potentials, labeled by growing values of the magnetic field condenses towards a certain limiting, magnetic-field-independent potential-distance curve. The limiting values of even ground-state energies are determined for four magnetic quantum numbers using the Karnakov–Popov method.

scholarly journals THE ENERGY EIGENVALUES OF THE TWO DIMENSIONAL HYDROGEN ATOM IN A MAGNETIC FIELD

2006 ◽  
Vol 15 (06) ◽  
pp. 1263-1271 ◽  
Author(s):  
A. SOYLU ◽  
O. BAYRAK ◽  
I. BOZTOSUN
Keyword(s):  
Magnetic Field ◽  
Hydrogen Atom ◽  
Iteration Method ◽  
Weak Magnetic Field ◽  
The Other ◽  
Asymptotic Iteration Method ◽  
Iterative Approach ◽  
Two Dimensional ◽  
Energy Eigenvalues ◽  
The Magnetic Field

In this paper, the energy eigenvalues of the two dimensional hydrogen atom are presented for the arbitrary Larmor frequencies by using the asymptotic iteration method. We first show the energy eigenvalues for the case with no magnetic field analytically, and then we obtain the energy eigenvalues for the strong and weak magnetic field cases within an iterative approach for n=2-10 and m=0-1 states for several different arbitrary Larmor frequencies. The effect of the magnetic field on the energy eigenvalues is determined precisely. The results are in excellent agreement with the findings of the other methods and our method works for the cases where the others fail.

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

Universe ◽  
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.

scholarly journals Rotating Melvin-like Universes and Wormholes in General Relativity

Symmetry ◽  
2020 ◽  
Vol 12 (8) ◽  
pp. 1306
Author(s):  
Kirill Bronnikov ◽  
Vladimir Krechet ◽  
Vadim Oshurko
Keyword(s):  
Magnetic Field ◽  
General Relativity ◽  
Equation Of State ◽  
Symmetry Axis ◽  
Energy Condition ◽  
Flat Space ◽  
Stiff Matter ◽  
Cylindrically Symmetric ◽  
The One ◽  
The Magnetic Field

We find a family of exact solutions to the Einstein–Maxwell equations for rotating cylindrically symmetric distributions of a perfect fluid with the equation of state p=wρ (|w|<1), carrying a circular electric current in the angular direction. This current creates a magnetic field along the z axis. Some of the solutions describe geometries resembling that of Melvin’s static magnetic universe and contain a regular symmetry axis, while some others (in the case w>0) describe traversable wormhole geometries which do not contain a symmetry axis. Unlike Melvin’s solution, those with rotation and a magnetic field cannot be vacuum and require a current. The wormhole solutions admit matching with flat-space regions on both sides of the throat, thus forming a cylindrical wormhole configuration potentially visible for distant observers residing in flat or weakly curved parts of space. The thin shells, located at junctions between the inner (wormhole) and outer (flat) regions, consist of matter satisfying the Weak Energy Condition under a proper choice of the free parameters of the model, which thus forms new examples of phantom-free wormhole models in general relativity. In the limit w→1, the magnetic field tends to zero, and the wormhole model tends to the one obtained previously, where the source of gravity is stiff matter with the equation of state p=ρ.

scholarly journals Equation of State of a Magnetized Dense Neutron System

Universe ◽  
2019 ◽  
Vol 5 (5) ◽  
pp. 104 ◽  
Author(s):  
Efrain J. Ferrer ◽  
Aric Hackebill
Keyword(s):  
Magnetic Field ◽  
Equation Of State ◽  
Chemical Potential ◽  
Compact Objects ◽  
Field Direction ◽  
Neutron Density ◽  
Magnetic Field Direction ◽  
System Equation ◽  
The One ◽  
The Magnetic Field

We discuss how a magnetic field can affect the equation of state of a many-particle neutron system. We show that, due to the anisotropy in the pressures, the pressure transverse to the magnetic field direction increases with the magnetic field, while the one along the field direction decreases. We also show that in this medium there exists a significant negative field-dependent contribution associated with the vacuum pressure. This negative pressure demands a neutron density sufficiently high (corresponding to a baryonic chemical potential of μ = 2.25 GeV) to produce the necessary positive matter pressure that can compensate for the gravitational pull. The decrease of the parallel pressure with the field limits the maximum magnetic field to a value of the order of 10 18 G, where the pressure decays to zero. We show that the combination of all these effects produces an insignificant variation of the system equation of state. We also found that this neutron system exhibits paramagnetic behavior expressed by the Curie’s law in the high-temperature regime. The reported results may be of interest for the astrophysics of compact objects such as magnetars, which are endowed with substantial magnetic fields.

scholarly journals Spin Polarization Oscillations and Coherence Time in the Random Interaction Approach

2019 ◽  
Vol 2019 ◽  
pp. 1-10
Author(s):  
P. Pereyra
Keyword(s):  
Magnetic Field ◽  
Time Evolution ◽  
Spin Polarization ◽  
Energy Levels ◽  
Coherence Time ◽  
Environment Interaction ◽  
Interaction Picture ◽  
Gaussian Orthogonal Ensemble ◽  
Interaction Approach ◽  
The Magnetic Field

We study the time evolution of the survival probability and the spin polarization of a dissipative nondegenerate two-level system in the presence of a magnetic field in the Faraday configuration. We apply the Extended Gaussian Orthogonal Ensemble approach to model the stochastic system-environment interaction and calculate the survival and spin polarization to first and second order of the interaction picture. We present also the time evolution of the thermal average of these quantities as functions of the temperature, the magnetic field, and the energy-levels density, for ρ(ϵ)∝ϵs, in the subohmic, ohmic, and superohmic dissipation forms. We show that the behavior of the spin polarization calculated here agrees rather well with the time evolution of spin polarization observed and calculated, recently, for the electron-nucleus dynamics of Ga centers in dilute (Ga,N)As semiconductors.

The Culgoora Magnetograph

1971 ◽  
Vol 43 ◽  
pp. 24-29 ◽  
Author(s):  
J. V. Ramsay ◽  
R. G. Giovanelli ◽  
H. R. Gillett
Keyword(s):  
Magnetic Field ◽  
High Resolution ◽  
Angular Resolution ◽  
Field Of View ◽  
Large Field ◽  
Sensitive Line ◽  
The One ◽  
The Magnetic Field

The magnetograph is based on a high-resolution filter which serves in place of a spectrograph, except that a reasonably large field of view (one-quarter of the Sun's diameter) can be observed at the one instant. Observations are made by obtaining filtergrams of opposite circular polarizations simultaneously in the wing of a magnetically sensitive line. Exposure times are about 0.3 s, the angular resolution of the magnetic field is about 2 arc s, closest frame repetition rates about 8 s. The filtergrams are processed subsequently by photographic or television subtraction. Semiautomatic photographic and/or TV subtractions yield magnetograms suitable for cinematographic projection though the subtractions are not yet as perfect as those obtained by individual subtraction.

Effect of temperature on magnetic susceptibility and thermodynamic properties of an asymmetric quantum dot in tilted magnetic field

2015 ◽  
Vol 29 (23) ◽  
pp. 1550127 ◽  
Author(s):  
R. Khordad
Keyword(s):  
Magnetic Field ◽  
Magnetic Susceptibility ◽  
Quantum Dot ◽  
Specific Heat ◽  
Energy Levels ◽  
Effect Of Temperature ◽  
Magnetic Field Direction ◽  
Asymmetric Quantum ◽  
Gaas Quantum Dot ◽  
The Magnetic Field

In this paper, the specific heat, entropy and magnetic susceptibility of an asymmetric GaAs quantum dot (QD) are studied under the influence of temperature and a tilted external magnetic field. We first calculate the analytical wave functions and energy levels using a transformation to simplify the Hamiltonian of the system. Then, we obtain the analytical expressions for specific heat, entropy and magnetic susceptibility as the function of temperature, magnetic field and its direction for various anisotropy of the system. According to the results obtained from the present work, we find that (i) the specific heat and entropy are decreased when the magnetic field increases. (ii) When anisotropy is increased, the specific heat and entropy decrease. (iii) At large magnetic fields, the anisotropy has not important effect on specific heat and entropy. In briefly, the magnetic field, magnetic field direction and anisotropy play important roles in the specific heat, entropy and magnetic susceptibility of an asymmetric QD.

Travelling fronts in nonlocal models for phase separation in an external field

1997 ◽  
Vol 127 (4) ◽  
pp. 823-835 ◽  
Author(s):  
Enza Orlandi ◽  
Livio Triolo
Keyword(s):  
Magnetic Field ◽  
Metastable Phase ◽  
Glauber Dynamics ◽  
One Dimensional ◽  
Kac Potentials ◽  
Nonlocal Models ◽  
Nonlocal Evolution Equation ◽  
Travelling Fronts ◽  
The One ◽  
The Magnetic Field

We consider the one-dimensional, nonlocal, evolution equation derived by De Masi et al. (1995) for Ising systems with Glauber dynamics, Kac potentials and magnetic field. We prove the existence of travelling fronts, their uniqueness modulo translations among the monotone profiles and their linear stability for all the admissible values of the magnetic field for which the underlying spin system exhibits a stable and metastable phase.

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