scholarly journals Description of the Magnetic Field and Divergence of Multisolenoid Aharonov-Bohm Potential

2016 ◽  
Vol 2016 ◽  
pp. 1-8 ◽  
Author(s):  
Araz R. Aliev ◽  
Elshad H. Eyvazov ◽  
Said F. M. Ibrahim ◽  
Hassan A. Zedan
Keyword(s):  
Magnetic Field ◽  
Finite Number ◽  
Differential Expression ◽  
Generalized Functions ◽  
Deficiency Index ◽  
Explicit Formulas ◽  
Minimal Operator ◽  
Bohm Potential ◽  
Aharonov Bohm ◽  
The Magnetic Field

Explicit formulas for the magnetic field and divergence of multisolenoid Aharonov-Bohm potential are obtained; the mathematical essence of this potential is explained. It is shown that the magnetic field and divergence of this potential are very singular generalized functions concentrated at a finite number of thin solenoids. Deficiency index is found for the minimal operator generated by the Aharonov-Bohm differential expression.

scholarly journals A general method for deriving vector potentials produced by knotted solenoids

2014 ◽  
Vol 29 (35) ◽  
pp. 1450189
Author(s):  
V. V. Sreedhar
Keyword(s):  
Magnetic Field ◽  
Charged Particles ◽  
Vector Potentials ◽  
Bohm Effect ◽  
Figure Eight Knot ◽  
Aharonov Bohm ◽  
The Magnetic Field ◽  
General Method

A general method for deriving exact expressions for vector potentials produced by arbitrarily knotted solenoids is presented. It consists of using simple physics ideas from magnetostatics to evaluate the magnetic field in a surrogate problem. The latter is obtained by modeling the knot with wire segments carrying steady currents on a cubical lattice. The expressions for a 31 (trefoil) and a 41 (figure-eight) knot are explicitly worked out. The results are of some importance in the study of the Aharonov–Bohm effect generalized to a situation in which charged particles moving through force-free regions are scattered by fluxes confined to the interior of knotted impenetrable tubes.

THE AHARONOV-CASHER AND BERRY’S PHASE EFFECTS IN SOLIDS

1991 ◽  
Vol 05 (23) ◽  
pp. 1607-1611 ◽  
Author(s):  
E.N. BOGACHEK ◽  
I.V. KRIVE ◽  
I.O. KULIK ◽  
A.S. ROZHAVSKY
Keyword(s):  
Magnetic Field ◽  
Phase Shift ◽  
Condensed Matter ◽  
Field Vector ◽  
Metal Ring ◽  
Topological Phase ◽  
Berry's Phase ◽  
Berry’S Phase ◽  
Aharonov Bohm ◽  
The Magnetic Field

We consider the manifestations of charge-induced topological phase shift (Aharonov-Casher effect) in condensed matter physics. There will be an oscillating response to high voltage of the magnetic moment (persistent current) and conductivity, as well as a phase shift of the Aharonov-Bohm oscillation to a smaller voltage, for the normal metal ring threaded by a charged fiber. These oscillations shift in phase if the magnetic field vector rotates along the ring, as a consequence of the geometrical (Berry’s) phase associated with the electron spin.

Electron Phase Microscopy of Magnetic Fields in Ferromagnets and Superconductors

2011 ◽  
Vol 1318 ◽  
Author(s):  
Akira Tonomura
Keyword(s):  
Magnetic Field ◽  
Magnetic Fields ◽  
Colossal Magnetoresistance ◽  
Layer Plane ◽  
Perpendicular Recording ◽  
High Tc ◽  
Phase Microscopy ◽  
Highly Sensitive ◽  
Aharonov Bohm ◽  
The Magnetic Field

ABSTRACTHighly sensitive electron phase microscopy based on the Aharonov-Bohm (AB) effect principle has been used to observe microscopic distributions of magnetic fields in ferromagnets and superconductors. The observation examples include the unconventional behaviors of interlayer Josephson vortices in anisotropic layered high-Tc superconducting YBa2Cu3O7-δ (YBCO) thin films, which are produced when the applied magnetic field is greatly tilted to the layer plane, and the magnetic-field distributions of tiny magnetic heads for perpendicular recording and of colossal magnetoresistance (CMR) materials.

scholarly journals Is the Magnetic Field Necessary for the Aharonov-Bohm Effect in Mesoscopics?

1998 ◽  
Vol 80 (11) ◽  
pp. 2417-2420 ◽  
Author(s):  
I. D. Vagner ◽  
A. S. Rozhavsky ◽  
P. Wyder ◽  
A. Yu. Zyuzin
Keyword(s):  
Magnetic Field ◽  
Bohm Effect ◽  
Aharonov Bohm ◽  
The Magnetic Field

NUMERICAL STUDY OF TRANSPORT PROPERTIES IN TOPOLOGICAL INSULATOR QUANTUM DOTS UNDER MAGNETIC FIELD

2013 ◽  
Vol 27 (14) ◽  
pp. 1350104 ◽  
Author(s):  
SHENG-NAN ZHANG ◽  
HUA JIANG ◽  
HAIWEN LIU
Keyword(s):  
Magnetic Field ◽  
Quantum Dots ◽  
Transport Properties ◽  
Topological Insulator ◽  
Numerical Study ◽  
Spin Polarized ◽  
Full Band ◽  
Spin Degeneracy ◽  
Aharonov Bohm ◽  
The Magnetic Field

In this paper, we investigate the transport properties of HgTe / CdTe -based topological insulator quantum dots (TIQDs) under magnetic field. Both disk and square shaped TIQDs are considered and the magneto-conductance are calculated numerically for various magnetic field strength. The magnetic field lifts the spin degeneracy, leading to spin polarized current at given Fermi energy. Meanwhile, the magneto-conductance demonstrates the Aharonov–Bohm (AB) oscillation with a period of one flux quantum [Formula: see text]. Numerical results for AB oscillation features indicate the mismatch between electron (e) and hole (h) doping conditions, which can be attributed to the e–h asymmetry in the full band Hamiltonian. Further, interference effect emerges around bulk and edge energy degenerate points, subsequently suppressing the magneto-conductance in both shaped systems. All these physical characteristics are qualitatively consistent for disk and square shaped TIQDs due to the topological nature of edge modes.

scholarly journals Hardy inequalities for Landau Hamiltonian and for Baouendi-Grushin operator with Aharonov-Bohm type magnetic field. Part I

2019 ◽  
Vol 125 (2) ◽  
pp. 239-269 ◽  
Author(s):  
Ari Laptev ◽  
Michael Ruzhansky ◽  
Nurgissa Yessirkegenov
Keyword(s):  
Magnetic Field ◽  
Quadratic Form ◽  
Type Inequality ◽  
Hardy Inequalities ◽  
Landau Hamiltonian ◽  
Grushin Operator ◽  
Aharonov Bohm ◽  
The Magnetic Field

In this paper we prove the Hardy inequalities for the quadratic form of the Laplacian with the Landau Hamiltonian type magnetic field. Moreover, we obtain a Poincaré type inequality and inequalities with more general families of weights. Furthermore, we establish weighted Hardy inequalities for the quadratic form of the magnetic Baouendi-Grushin operator for the magnetic field of Aharonov-Bohm type. For these, we show refinements of the known Hardy inequalities for the Baouendi-Grushin operator involving radial derivatives in some of the variables. The corresponding uncertainty type principles are also obtained.

scholarly journals Self-adjoint Extensions of Schrödinger Operators with ?-magnetic Fields on Riemannian Manifolds

10.14311/1271 ◽  
2010 ◽  
Vol 50 (5) ◽  
Author(s):  
T. Mine
Keyword(s):  
Magnetic Field ◽  
Riemannian Manifold ◽  
Magnetic Fields ◽  
Boundary Conditions ◽  
Riemannian Manifolds ◽  
Complete Characterization ◽  
The Self ◽  
Minimal Operator ◽  
The Magnetic Field

We consider the magnetic Schr¨odinger operator on a Riemannian manifold M. We assume the magnetic field is given by the sum of a regular field and the Dirac δ measures supported on a discrete set Γ in M. We give a complete characterization of the self-adjoint extensions of the minimal operator, in terms of the boundary conditions. The result is an extension of the former results by Dabrowski-Šťoviček and Exner-Šťoviček-Vytřas.

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.

scholarly journals Inverse problems for Aharonov–Bohm rings

2009 ◽  
Vol 148 (2) ◽  
pp. 331-362 ◽  
Author(s):  
P. KURASOV
Keyword(s):  
Magnetic Field ◽  
Inverse Problem ◽  
Matrix Function ◽  
Characteristic Zero ◽  
Resonance Condition ◽  
Metric Graphs ◽  
Weyl Matrix ◽  
Dirichlet To Neumann Map ◽  
Aharonov Bohm ◽  
The Magnetic Field

AbstractThe inverse problem for Schrödinger operators on metric graphs is investigated in the presence of magnetic field. Graphs without loops and with Euler characteristic zero are considered. It is shown that the knowledge of the Titchmarsh–Weyl matrix function (Dirichlet-to-Neumann map) for just two values of the magnetic field allows one to reconstruct the graph and potential on it provided a certain additional no-resonance condition is satisfied.

Resonant interaction of runaway electrons with magnetic field ripple in tokamak plasmas

2009 ◽  
Vol 75 (5) ◽  
pp. 669-674 ◽  
Author(s):  
Z. Y. CHEN ◽  
B. N. WAN ◽  
Y. J. SHI ◽  
H. J. JU ◽  
J. X. ZHU ◽  
...  
Keyword(s):  
Magnetic Field ◽  
Finite Number ◽  
Resonant Interaction ◽  
Maximum Energy ◽  
Toroidal Magnetic Field ◽  
Tokamak Plasmas ◽  
Edge Region ◽  
Runaway Electrons ◽  
The Magnetic Field

AbstractThe toroidal magnetic field of tokamaks is generated by a finite number of coils, which slightly modulates the magnetic field and runaway electrons experience this modulation. The resonant interaction between runaway electrons and the magnetic field ripple has been observed in the HT-7 tokamak. The maximum energy of runaways in the edge region could be blocked by the resonance of gyromotion with the nth harmonic of the magnetic field ripple. This resonant interaction is favorable for the control of runaway energy.

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