Energy of Surface States for 3D Magnetic Schrödinger Operators

Nasrallah, Marwa

doi:10.1007/s12220-015-9597-3

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Cited by 2 publications

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“…The discussion in this paper is limited for planar domains. Extensions to higher dimensions does not seem trivial; [29] contains results for the Neumann condition in 3D domains.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Semi-classical trace asymptotics for magnetic Schrödinger operators with Robin condition

Kachmar

Nasrallah

2015

Journal of Mathematical Physics

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Abstract. We compute the sum and number of eigenvalues for a certain class of magnetic Schrödinger operators in a domain with boundary. Functions in the domain of the operator satisfy a (magnetic) Robin condition. The calculations are valid in the semi-classical asymptotic limit and the eigenvalues concerned correspond to eigenstates localized near the boundary of the domain. The formulas we derive display the influence of the boundary and the boundary condition and are valid under a weak regularity assumption of the boundary function. Our approach relies on three main points: reduction to the boundary; construction of boundary coherent states; handling the boundary term as a surface electric potential and controlling the errors by various Lieb-Thirring inequalities.

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“…The discussion in this paper is limited for planar domains. Extensions to higher dimensions does not seem trivial; [29] contains results for the Neumann condition in 3D domains.…”

Section: Introductionmentioning

confidence: 99%

“…Differentiation of the formulas in Theorem 1.1 with respect to λh yields a formula for the number of eigenvalues. See [9,29] for a precise statement of this technique. The formulas for the number of eigenvalues are collected in: Corollary 1.2.…”

Section: Introductionmentioning

confidence: 99%