The Landau Hamiltonian with δ-potentials supported on curves

2019 ◽  
Vol 32 (04) ◽  
pp. 2050010
Author(s):  
Jussi Behrndt ◽  
Pavel Exner ◽  
Markus Holzmann ◽  
Vladimir Lotoreichik
Keyword(s):  
Magnetic Field ◽  
Spectral Properties ◽  
Accumulation Rate ◽  
Smooth Curve ◽  
Homogeneous Magnetic Field ◽  
Quantum Systems ◽  
Real Coefficient ◽  
Landau Levels ◽  
Singularly Perturbed ◽  
Landau Hamiltonian

The spectral properties of the singularly perturbed self-adjoint Landau Hamiltonian [Formula: see text] in [Formula: see text] with a [Formula: see text]-potential supported on a finite [Formula: see text]-smooth curve [Formula: see text] are studied. Here [Formula: see text] is the vector potential, [Formula: see text] is the strength of the homogeneous magnetic field, and [Formula: see text] is a position-dependent real coefficient modeling the strength of the singular interaction on the curve [Formula: see text]. After a general discussion of the qualitative spectral properties of [Formula: see text] and its resolvent, one of the main objectives in the present paper is a local spectral analysis of [Formula: see text] near the Landau levels [Formula: see text], [Formula: see text]. Under various conditions on [Formula: see text], it is shown that the perturbation smears the Landau levels into eigenvalue clusters, and the accumulation rate of the eigenvalues within these clusters is determined in terms of the capacity of the support of [Formula: see text]. Furthermore, the use of Landau Hamiltonians with [Formula: see text]-perturbations as model operators for more realistic quantum systems is justified by showing that [Formula: see text] can be approximated in the norm resolvent sense by a family of Landau Hamiltonians with suitably scaled regular potentials.

scholarly journals Nonrelativistic anti-Snyder model and some applications

2017 ◽  
Vol 32 (02n03) ◽  
pp. 1750009 ◽  
Author(s):  
C. L. Ching ◽  
C. X. Yeo ◽  
W. K. Ng
Keyword(s):  
Magnetic Field ◽  
Quantum Mechanics ◽  
Bound States ◽  
Homogeneous Magnetic Field ◽  
Maximum Energy ◽  
Minimal Length ◽  
Landau Levels ◽  
Space Representation ◽  
Free Particles ◽  
Ordinary Quantum

In this paper, we examine the (2[Formula: see text]+[Formula: see text]1)-dimensional Dirac equation in a homogeneous magnetic field under the nonrelativistic anti-Snyder model which is relevant to doubly/deformed special relativity (DSR) since it exhibits an intrinsic upper bound of the momentum of free particles. After setting up the formalism, exact eigensolutions are derived in momentum space representation and they are expressed in terms of finite orthogonal Romanovski polynomials. There is a finite maximum number of allowable bound states [Formula: see text] due to the orthogonality of the polynomials and the maximum energy is truncated at [Formula: see text]. Similar to the minimal length case, the degeneracy of the Dirac–Landau levels in anti-Snyder model are modified and there are states that do not exist in the ordinary quantum mechanics limit [Formula: see text]. By taking [Formula: see text], we explore the motion of effective massless charged fermions in graphene-like material and obtained a maximum bound of deformed parameter [Formula: see text]. Furthermore, we consider the modified energy dispersion relations and its application in describing the behavior of neutrinos oscillation under modified commutation relations.

PERIODIC AHARONOV–BOHM SOLENOIDS IN A CONSTANT MAGNETIC FIELD

2006 ◽  
Vol 18 (08) ◽  
pp. 913-934 ◽  
Author(s):  
TAKUYA MINE ◽  
YUJI NOMURA
Keyword(s):  
Magnetic Field ◽  
Landau Level ◽  
Density Of States ◽  
Homogeneous Magnetic Field ◽  
Landau Levels ◽  
Sufficient Condition ◽  
Absolutely Continuous ◽  
Lowest Landau Level ◽  
Aharonov Bohm ◽  
The Magnetic Field

We consider the magnetic Schrödinger operator on R2. The magnetic field is the sum of a homogeneous magnetic field and periodically varying pointlike magnetic fields on a lattice. We shall give a sufficient condition for each Landau level to be an infinitely degenerated eigenvalue. This condition is also necessary for the lowest Landau level. In the threshold case, we see that the spectrum near the lowest Landau level is purely absolutely continuous. Moreover, we shall give an estimate for the density of states for Landau levels and their gaps. The proof is based on the method of Geyler and Šťovíček, the magnetic Bloch theory, and canonical commutation relations.

Analysis of magneto rheological elastomers for energy harvesting systems

2020 ◽  
Vol 64 (1-4) ◽  
pp. 439-446
Author(s):  
Gildas Diguet ◽  
Gael Sebald ◽  
Masami Nakano ◽  
Mickaël Lallart ◽  
Jean-Yves Cavaillé
Keyword(s):  
Magnetic Field ◽  
Energy Harvesting ◽  
Shear Strain ◽  
Magnetic Induction ◽  
Magnetic Particles ◽  
Homogeneous Magnetic Field ◽  
Electrical Signal ◽  
Harvesting Systems ◽  
Dc Bias ◽  
Magneto Rheological

Magneto Rheological Elastomers (MREs) are composite materials based on an elastomer filled by magnetic particles. Anisotropic MRE can be easily manufactured by curing the material under homogeneous magnetic field which creates column of particles. The magnetic and elastic properties are actually coupled making these MREs suitable for energy conversion. From these remarkable properties, an energy harvesting device is considered through the application of a DC bias magnetic induction on two MREs as a metal piece is applying an AC shear strain on them. Such strain therefore changes the permeabilities of the elastomers, hence generating an AC magnetic induction which can be converted into AC electrical signal with the help of a coil. The device is simulated with a Finite Element Method software to examine the effect of the MRE parameters, the DC bias magnetic induction and applied shear strain (amplitude and frequency) on the resulting electrical signal.

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

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.

Notizen: Effect of Magnetic Field on Ascorbic Acid Oxidase Activity, I

1986 ◽  
Vol 41 (3) ◽  
pp. 355-358 ◽  
Author(s):  
V. S. Ghole ◽  
P. S. Damle ◽  
W. H.-P. Thiemann
Keyword(s):  
Magnetic Field ◽  
Ascorbic Acid ◽  
Homogeneous Magnetic Field ◽  
Acid Oxidase ◽  
High Substrate Concentration ◽  
Ascorbic Acid Oxidase ◽  
Rate Of Reaction ◽  
Substrate Concentrations ◽  
Burk Plot

A homogeneous magnetic field of 1.1 T strength exhibits a significant influence on the activity of the enzyme ascorbic acid oxidase in vitro. A Lineweaver-Burk plot of the reaction shows the typical pattern of a mixed-type inhibition, i.e. a larger rate of reaction at low substrate concentrations and a smaller rate of reaction at high substrate concentration than that of the control without magnetic field applied.

scholarly journals Finite Element Analysis of Magnetic Field Exciter for Direct Testing of Magnetocaloric Materials’ Properties

Energies ◽  
2021 ◽  
Vol 14 (10) ◽  
pp. 2792
Author(s):  
Wieslaw Lyskawinski ◽  
Wojciech Szelag ◽  
Cezary Jedryczka ◽  
Tomasz Tolinski
Keyword(s):  
Magnetic Field ◽  
Finite Element ◽  
Magnetic Circuit ◽  
Homogeneous Magnetic Field ◽  
Element Analysis ◽  
Mcm Testing ◽  
Testing Region ◽  
Magnetocaloric Materials ◽  
Field Excitation ◽  
The Magnetic Field

The paper presents research on magnetic field exciters dedicated to testing magnetocaloric materials (MCMs) as well as used in the design process of magnetic refrigeration systems. An important element of the proposed test stand is the system of magnetic field excitation. It should provide a homogeneous magnetic field with a controllable value of its intensity in the MCM testing region. Several concepts of a magnetic circuit when designing the field exciters have been proposed and evaluated. In the MCM testing region of the proposed exciters, the magnetic field is controlled by changing the structure of the magnetic circuit. A precise 3D field model of electromagnetic phenomena has been developed in the professional finite element method (FEM) package and used to design and analyze the exciters. The obtained results of the calculations of the magnetic field distribution in the working area were compared with the results of the measurements carried out on the exciter prototype. The conclusions resulting from the conducted research are presented and discussed.

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