scholarly journals Stability of eigenvalues of quantum graphs with respect to magnetic perturbation and the nodal count of the eigenfunctions

2014 ◽  
Vol 372 (2007) ◽  
pp. 20120522 ◽  
Author(s):  
Gregory Berkolaiko ◽  
Tracy Weyand
Keyword(s):  
Magnetic Field ◽  
Morse Index ◽  
Magnetic Potential ◽  
Zero Magnetic Field ◽  
Quantum Graphs ◽  
Nodal Count ◽  
Magnetic Perturbation ◽  
Number Of Zeros ◽  
Stability Of Eigenvalues ◽  
The Stability

We prove an analogue of the magnetic nodal theorem on quantum graphs: the number of zeros ϕ of the n th eigenfunction of the Schrödinger operator on a quantum graph is related to the stability of the n th eigenvalue of the perturbation of the operator by magnetic potential. More precisely, we consider the n th eigenvalue as a function of the magnetic perturbation and show that its Morse index at zero magnetic field is equal to ϕ −( n −1).

scholarly journals Edge pinch instability of oblate liquid metal drops in a transverse AC magnetic field

2011 ◽  
Vol 676 ◽  
pp. 218-236 ◽  
Author(s):  
JĀNIS PRIEDE
Keyword(s):  
Magnetic Field ◽  
Liquid Metal ◽  
Rotational Symmetry ◽  
Initial Perturbation ◽  
Magnetic Potential ◽  
Surface Integral ◽  
Ac Magnetic Field ◽  
Scalar Magnetic Potential ◽  
Equilibrium Shapes ◽  
The Stability

This paper considers the stability of liquid metal drops subject to a high-frequency AC magnetic field. An energy variation principle is derived in terms of the surface integral of the scalar magnetic potential. This principle is applied to a thin perfectly conducting liquid disk, which is used to model the drops constrained in a horizontal gap between two parallel insulating plates. Firstly, the stability of a circular disk is analysed with respect to small-amplitude harmonic edge perturbations. Analytical solution shows that the edge deformations with the azimuthal wavenumbers m = 2, 3, 4, . . . start to develop as the magnetic Bond number exceeds the critical threshold Bmc = 3π(m + 1)/2. The most unstable is m = 2 mode, which corresponds to an elliptical deformation. Secondly, strongly deformed equilibrium shapes are modelled numerically by minimising the associated energy in combination with the solution of a surface integral equation for the scalar magnetic potential on an unstructured triangular mesh. The edge instability is found to result in the equilibrium shapes of either two- or threefold rotational symmetry depending on the magnetic field strength and the initial perturbation. The shapes of higher rotational symmetries are unstable and fall back to one of these two basic states. The developed method is both efficient and accurate enough for modelling of strongly deformed drop shapes.

STRANGE QUARK MATTER IN STRONG MAGNETIC FIELD

1994 ◽  
Vol 09 (39) ◽  
pp. 3611-3618 ◽  
Author(s):  
SOMENATH CHAKRABARTY ◽  
ASHOK GOYAL
Keyword(s):  
Magnetic Field ◽  
Strong Magnetic Field ◽  
Quark Matter ◽  
Strange Quark ◽  
Critical Value ◽  
Strange Quark Matter ◽  
Zero Magnetic Field ◽  
Zero Temperature ◽  
Mit Bag Model ◽  
The Stability

Using conventional MIT bag model of confinement, the stability of bulk strange quark matter (SQM) in the presence of a strong magnetic field at zero temperature and zero pressure has been investigated. The binding energy of SQM increases in the presence of strong magnetic field greater than or of the order of some critical value at which the cyclotron lines begin to occur. At finite temperature the pressure dependence of the system has also been presented, which differs significantly from zero magnetic field case.

scholarly journals Experimental signatures of nodeless multiband superconductivity in a $$\hbox {2H-Pd}_{0.08} \hbox {TaSe}_2$$ single crystal

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Chanhee Kim ◽  
Dilip Bhoi ◽  
Yeahan Sur ◽  
Byung-Gu Jeon ◽  
Dirk Wulferding ◽  
...  
Keyword(s):  
Magnetic Field ◽  
Single Crystal ◽  
Zero Magnetic Field ◽  
Anisotropy Ratio ◽  
Strong Temperature Dependence ◽  
Critical Fields ◽  
Band Theory ◽  
Plane Field ◽  
Low Field ◽  
Out Of Plane

AbstractIn order to understand the superconducting gap nature of a $$\hbox {2H-Pd}_{0.08} \hbox {TaSe}_2$$ 2H-Pd 0.08 TaSe 2 single crystal with $$T_{c} = 3.13 \text { K}$$ T c = 3.13 K , in-plane thermal conductivity $$\kappa $$ κ , in-plane London penetration depth $$\lambda _{\text {L}}$$ λ L , and the upper critical fields $$H_{c2}$$ H c 2 have been investigated. At zero magnetic field, it is found that no residual linear term $$\kappa _{0}/T$$ κ 0 / T exists and $$\lambda _{\text {L}}$$ λ L follows a power-law $$T^n$$ T n (T: temperature) with n = 2.66 at $$T \le \frac{1}{3}T_c$$ T ≤ 1 3 T c , supporting nodeless superconductivity. Moreover, the magnetic-field dependence of $$\kappa _{0}$$ κ 0 /T clearly shows a shoulder-like feature at a low field region. The temperature dependent $$H_{c2}$$ H c 2 curves for both in-plane and out-of-plane field directions exhibit clear upward curvatures near $$T_c$$ T c , consistent with the shape predicted by the two-band theory and the anisotropy ratio between the $$H_{c2}$$ H c 2 (T) curves exhibits strong temperature-dependence. All these results coherently suggest that $$\hbox {2H-Pd}_{0.08} \hbox {TaSe}_2$$ 2H-Pd 0.08 TaSe 2 is a nodeless, multiband superconductor.

scholarly journals Imaging the formation and surface phase separation of the CE phase

2021 ◽  
Vol 6 (1) ◽  
Author(s):  
Haibiao Zhou ◽  
Qiyuan Feng ◽  
Yubin Hou ◽  
Masao Nakamura ◽  
Yoshinori Tokura ◽  
...  
Keyword(s):  
Magnetic Field ◽  
Phase Transitions ◽  
Charge Ordering ◽  
Zero Magnetic Field ◽  
Ferromagnetic Phase ◽  
Emergent Properties ◽  
Orbital Ordering ◽  
Strong Electron ◽  
Antiferromagnetic Correlation ◽  
Ordering Transitions

AbstractThe CE phase is an extraordinary phase exhibiting the simultaneous spin, charge, and orbital ordering due to strong electron correlation. It is an ideal platform to investigate the role of the multiple orderings in the phase transitions and discover emergent properties. Here, we use a cryogenic high-field magnetic force microscope to image the phase transitions and properties of the CE phase in a Pr0.5Ca0.5MnO3 thin film. In a high magnetic field, we observed a clear suppression of magnetic susceptibility at the charge-ordering insulator transition temperature (TCOI), whereas, at the Néel temperature (TN), no significant change is observed. This observation favors the scenario of strong antiferromagnetic correlation developed below TCOI but raises questions about the Zener polaron paramagnetic phase picture. Besides, we discoverd a phase-separated surface state in the CE phase regime. Ferromagnetic phase domains residing at the surface already exist in zero magnetic field and show ultra-high magnetic anisotropy. Our results provide microscopic insights into the unconventional spin- and charge-ordering transitions and revealed essential attributes of the CE phase, highlighting unusual behaviors when multiple electronic orderings are involved.

scholarly journals Stability of nonaxisymmetric ferrofluid flow in rotating cylinders with magnetic field

2005 ◽  
Vol 2005 (23) ◽  
pp. 3727-3737 ◽  
Author(s):  
Jitender Singh ◽  
Renu Bajaj
Keyword(s):  
Magnetic Field ◽  
Applied Magnetic Field ◽  
Critical Value ◽  
Annular Space ◽  
Rotating Cylinders ◽  
The Stability

Effect of an axially applied magnetic field on the stability of a ferrofluid flow in an annular space between two coaxially rotating cylinders with nonaxisymmetric disturbances has been investigated numerically. The critical value of the ratioΩ∗of angular speeds of the two cylinders, at the onset of the first nonaxisymmetric mode of disturbance, has been observed to be affected by the applied magnetic field.

scholarly journals Colossal anomalous Nernst effect in a correlated noncentrosymmetric kagome ferromagnet

2021 ◽  
Vol 7 (13) ◽  
pp. eabf1467
Author(s):  
T. Asaba ◽  
V. Ivanov ◽  
S. M. Thomas ◽  
S. Y. Savrasov ◽  
J. D. Thompson ◽  
...  
Keyword(s):  
Magnetic Field ◽  
Electronic Structure ◽  
Theoretical Calculations ◽  
Zero Magnetic Field ◽  
Nernst Effect ◽  
Nodal Lines ◽  
Transverse Response ◽  
Narrow Bands ◽  
Strong Spin ◽  
Anomalous Nernst Effect

The transverse voltage generated by a temperature gradient in a perpendicularly applied magnetic field, termed the Nernst effect, has promise for thermoelectric applications and for probing electronic structure. In magnetic materials, an anomalous Nernst effect (ANE) is possible in a zero magnetic field. We report a colossal ANE in the ferromagnetic metal UCo0.8Ru0.2Al, reaching 23 microvolts per kelvin. Uranium’s 5f electrons provide strong electronic correlations that lead to narrow bands, a known route to producing a large thermoelectric response. In addition, uranium’s strong spin-orbit coupling produces an intrinsic transverse response in this material due to the Berry curvature associated with the relativistic electronic structure. Theoretical calculations show that in UCo0.8Ru0.2Al at least 148 Weyl nodes, and two nodal lines, exist within 60 millielectron volt of the Fermi level. This work demonstrates that magnetic actinide materials can host strong Nernst and Hall responses due to their combined correlated and topological nature.

scholarly journals No-z Model for Magnetic Fields of Different Astrophysical Objects and Stability of the Solutions

Data ◽  
2021 ◽  
Vol 6 (1) ◽  
pp. 4
Author(s):  
Evgeny Mikhailov ◽  
Daniela Boneva ◽  
Maria Pashentseva
Keyword(s):  
Magnetic Field ◽  
Magnetic Fields ◽  
Large Scale ◽  
Point Of View ◽  
Accretion Discs ◽  
Wide Range ◽  
Astrophysical Objects ◽  
Alpha Effect ◽  
The Stability ◽  
The Magnetic Field

A wide range of astrophysical objects, such as the Sun, galaxies, stars, planets, accretion discs etc., have large-scale magnetic fields. Their generation is often based on the dynamo mechanism, which is connected with joint action of the alpha-effect and differential rotation. They compete with the turbulent diffusion. If the dynamo is intensive enough, the magnetic field grows, else it decays. The magnetic field evolution is described by Steenbeck—Krause—Raedler equations, which are quite difficult to be solved. So, for different objects, specific two-dimensional models are used. As for thin discs (this shape corresponds to galaxies and accretion discs), usually, no-z approximation is used. Some of the partial derivatives are changed by the algebraic expressions, and the solenoidality condition is taken into account as well. The field generation is restricted by the equipartition value and saturates if the field becomes comparable with it. From the point of view of mathematical physics, they can be characterized as stable points of the equations. The field can come to these values monotonously or have oscillations. It depends on the type of the stability of these points, whether it is a node or focus. Here, we study the stability of such points and give examples for astrophysical applications.

scholarly journals TRANSPORT PROPERTIES OF 2D ELECTRON GAS IN AN n-InGaAs/GaAs DQW IN A VICINITY OF LOW MAGNETIC-FIELD-INDUCED HALL INSULATOR–QUANTUM HALL LIQUID TRANSITION

2007 ◽  
Vol 06 (03n04) ◽  
pp. 173-177
Author(s):  
YU. G. ARAPOV ◽  
S. V. GUDINA ◽  
G. I. HARUS ◽  
V. N. NEVEROV ◽  
N. G. SHELUSHININA ◽  
...  
Keyword(s):  
Magnetic Field ◽  
Electron Gas ◽  
Quantum Hall ◽  
Zero Magnetic Field ◽  
Double Quantum ◽  
Ballistic Regime ◽  
2D Electron Gas ◽  
Double Quantum Well ◽  
Liquid Transition ◽  
Low Magnetic Field

The resistivity (ρ) of low mobility dilute 2D electron gas in an n- InGaAs / GaAs double quantum well (DQW) exhibits the monotonic "insulating-like" temperature dependence (dρ/dT < 0) at T = 1.8–70 K in zero magnetic field. This temperature interval corresponds to a ballistic regime (kBTτ/ħ > 0.1–3.5) for our samples, and the electron density is on an "insulating" side of the so-called B = 0 2D metal–insulator transition. We show that the observed features of localization and Landau quantization in a vicinity of the low magnetic-field-induced insulator–quantum Hall liquid transition is due to the σxy(T) anomalous T-dependence.

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