Non-homogeneous magnetic permeability and magnetic steps within the Ginzburg–Landau model

Assaad, Wafaa; Kashmar, Ayman; Sabbagh, Lamis

doi:10.1007/s41808-020-00077-7

Cited by 2 publications

(1 citation statement)

References 37 publications

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“…The 2D GL model was extensively used for constant/smooth external magnetic fields in the case of domains with smooth boundary [BS,LP1,HM1,HP,FH1,FH2,Ray,DR] or domains with corners [BN2,BND,BNDMV,B-NF] (see also [Cor,CG1,CG2,CG3,HK] for the phase preceding the transition to the normal state). Recently, 2D GL models with piecewise-constant magnetic fields were considered in [AK1,AKPS,As1,AKS,As2] both in a linear and non-linear framework, and H C 3 was examined in [As1].…”

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A 3D-Schroedinger operator under magnetic steps

Assaad¹,

Giacomelli²

2021

Preprint

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We consider Schrödinger operators on the space and the half-space with discontinuous magnetic fields having a piecewise-constant strength and a uniform direction. We aim at studying the infimum of the spectrum of the operator. Working in the halfspace, we further give sufficient conditions on the strength and the direction of the magnetic field such that the aforementioned infimum is an eigenvalue of a reduced model operator on the half-plane.where the material oscillates between the superconducting and normal states while increasing the intensity of the magnetic field. In the latter situations, HC 3 is not unique.

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confidence: 99%

A 3D-Schroedinger operator under magnetic steps

Assaad¹,

Giacomelli²

2021

Preprint

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Magnetic steps on the threshold of the normal state

Assaad

2020

Journal of Mathematical Physics

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Superconductivity in the presence of a step magnetic field has recently been the focus of many works. This contribution examines the behavior of a two-dimensional superconducting domain when superconductivity is lost in the whole domain except near the intersection points of the discontinuity edge and the boundary. The problem involves its own effective energy. We provide local estimates of the minimizers in the neighborhoods of the intersection points. Consequently, we introduce new critical fields marking the loss of superconductivity in the vicinity of these points. This study is modeled by the Ginzburg–Landau theory, and large Ginzburg–Landau parameters are considered.

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Non-homogeneous magnetic permeability and magnetic steps within the Ginzburg–Landau model

Cited by 2 publications

References 37 publications

A 3D-Schroedinger operator under magnetic steps

A 3D-Schroedinger operator under magnetic steps

Magnetic steps on the threshold of the normal state

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