scholarly journals Dirichlet and Neumann eigenvalues for half-plane magnetic Hamiltonians

2014 ◽  
Vol 26 (02) ◽  
pp. 1450003 ◽  
Author(s):  
Vincent Bruneau ◽  
Pablo Miranda ◽  
Georgi Raikov
Keyword(s):  
Magnetic Field ◽  
Asymptotic Behavior ◽  
Half Plane ◽  
Compact Support ◽  
Constant Magnetic Field ◽  
Scalar Potential ◽  
Neumann Boundary ◽  
Essential Spectra ◽  
Neumann Eigenvalues ◽  
Effective Hamiltonians

Let H0,D (respectively, H0,N) be the Schrödinger operator in constant magnetic field on the half-plane with Dirichlet (respectively, Neumann) boundary conditions, and let Hℓ := H0,ℓ - V, ℓ = D, N, where the scalar potential V is non-negative, bounded, does not vanish identically, and decays at infinity. We compare the distribution of the eigenvalues of HD and HN below the respective infima of the essential spectra. To this end, we construct effective Hamiltonians which govern the asymptotic behavior of the discrete spectrum of Hℓ near inf σ ess (Hℓ) = inf σ(H0,ℓ), ℓ = D, N. Applying these Hamiltonians, we show that σ disc (HD) is infinite even if V has a compact support, while σ disc (HN) could be finite or infinite depending on the decay rate of V.

scholarly journals QUASI-CLASSICAL VERSUS NON-CLASSICAL SPECTRAL ASYMPTOTICS FOR MAGNETIC SCHRÖDINGER OPERATORS WITH DECREASING ELECTRIC POTENTIALS

2002 ◽  
Vol 14 (10) ◽  
pp. 1051-1072 ◽  
Author(s):  
GEORGI D. RAIKOV ◽  
SIMONE WARZEL
Keyword(s):  
Magnetic Field ◽  
Asymptotic Behaviour ◽  
Discrete Spectrum ◽  
Essential Spectrum ◽  
Electric Potential ◽  
Compact Support ◽  
Constant Magnetic Field ◽  
Spectral Asymptotics ◽  
Boundary Points ◽  
Electric Potentials

We consider the Schrödinger operator H(V) on L2 (ℝ2) or L2(ℝ3) with constant magnetic field, and electric potential V which typically decays at infinity exponentially fast or has a compact support. We investigate the asymptotic behaviour of the discrete spectrum of H(V) near the boundary points of its essential spectrum. If the decay of V is Gaussian or faster, this behaviour is non-classical in the sense that it is not described by the quasi-classical formulas known for the case where V admits a power-like decay.

A CMT Device for Electric Energy Meter Detection

2020 ◽  
Vol 13 ◽  
Author(s):  
Zhi Zeng ◽  
Yongfu Zhou
Keyword(s):  
Magnetic Field ◽  
Constant Magnetic Field ◽  
Electromagnetic Interference ◽  
Production Efficiency ◽  
Electric Energy ◽  
Labor Cost ◽  
Automatic Testing ◽  
National Standard ◽  
Measurement Instruments ◽  
Detection Technology

Background: Detection technology is a product development technique that serves as a basis for quality assurance. As electric energy meters (EEMs) are measurement instruments whose use is mandatory in several nations, their accuracy, which directly depends on their reliability and proper functioning, is paramount. In this study, to eliminate electromagnetic interference, a device is developed for testing a set of EEMs under a constant magnetic field interference. The detection device can simultaneously test 6 electric meters; moreover, in the future, it will be able to measure the influence of magnetic field strength on the measurement accuracy of EEMs, thereby improving the production efficiency of electric meter manufacturers. Methods: In this study, we first design a 3D model of the detection device for a single meter component; then, we establish a network, which includes a control system, and perform the planning of the path of a block that generates a constant magnetic field. Finally, we control the three-axis motion and rotation of the block using a PLC to implement detection for the five sides of the EEM. Results & Discussion: The proposed device can accurately determine whether an EEM can adequately function, within the error range prescribed by a national standard, under electromagnetic interference; this can enable reliable, automatic testing and fault detection for EEMs. Experiments show that our device can decrease the labor cost for EEM manufacturers.

scholarly journals The internal conversion of gamma-rays.—Part II

1928 ◽  
Vol 121 (787) ◽  
pp. 447-456
Keyword(s):  
Magnetic Field ◽  
Quantum Mechanics ◽  
Wave Equation ◽  
Gamma Rays ◽  
Internal Conversion ◽  
Scalar Potential ◽  
X Ray ◽  
Electro Magnetic Field ◽  
Γ Rays ◽  
Electro Magnetic

In a previous paper the absorption of γ-rays in the K-X-ray levels of the atom in which they are emitted was calculated according to the Quantum Mechanics, supposing the γ-rays to be emitted from a doublet of moment f ( t ) at the centre of the atom. The non-relativity wave equation derived from the relativity wave equation for an electron of charge — ε moving in an electro-magnetic field of vector potential K and scalar potential V is h 2 ∇ 2 ϕ + 2μ ( ih ∂/∂ t + εV + ih ε/μ c (K. grad)) ϕ = 0. (1) Suppose, however, that K involves the space co-ordinates. Then, (K. grad) ϕ ≠ (grad . K) ϕ , and the expression (K . grad) ϕ is not Hermitic. Equation (1) cannot therefore be the correct non-relativity wave equation for a single electron in an electron agnetic field, and we must substitute h 2 ∇ 2 ϕ + 2μ ( ih ∂/∂ t + εV) ϕ + ih ε/ c ((K. grad) ϕ + (grad. K) ϕ ) = 0. (2)

scholarly journals Ground state and stability of the fractional plateau phase in metallic Shastry–Sutherland system TmB4

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Matúš Orendáč ◽  
Slavomír Gabáni ◽  
Pavol Farkašovský ◽  
Emil Gažo ◽  
Jozef Kačmarčík ◽  
...  
Keyword(s):  
Magnetic Field ◽  
Phase Diagram ◽  
Ground State ◽  
Constant Magnetic Field ◽  
Paramagnetic Phase ◽  
The Other ◽  
Zero Field ◽  
Plateau Phase ◽  
Low Field ◽  
Zero Field Cooling

AbstractWe present a study of the ground state and stability of the fractional plateau phase (FPP) with M/Msat = 1/8 in the metallic Shastry–Sutherland system TmB4. Magnetization (M) measurements show that the FPP states are thermodynamically stable when the sample is cooled in constant magnetic field from the paramagnetic phase to the ordered one at 2 K. On the other hand, after zero-field cooling and subsequent magnetization these states appear to be of dynamic origin. In this case the FPP states are closely associated with the half plateau phase (HPP, M/Msat = ½), mediate the HPP to the low-field antiferromagnetic (AF) phase and depend on the thermodynamic history. Thus, in the same place of the phase diagram both, the stable and the metastable (dynamic) fractional plateau (FP) states, can be observed, depending on the way they are reached. In case of metastable FP states thermodynamic paths are identified that lead to very flat fractional plateaus in the FPP. Moreover, with a further decrease of magnetic field also the low-field AF phase becomes influenced and exhibits a plateau of the order of 1/1000 Msat.

Structural studies of epoxy polymers cured in a constant magnetic field

1985 ◽  
Vol 20 (4) ◽  
pp. 402-405 ◽  
Author(s):  
T. A. Man'ko ◽  
A. N. Kvasha ◽  
A. V. Solov'ev ◽  
V. B. Shcheneva ◽  
I. M. Ermolaev
Keyword(s):  
Magnetic Field ◽  
Constant Magnetic Field ◽  
Structural Studies ◽  
Epoxy Polymers
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