Estimates for numbers of negative eigenvalues of Laplacian for Y-type chain of weakly coupled ball resonators

Melikhova, A.S.

doi:10.1142/9789814618144_0028

Cited by 1 publication

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References 6 publications

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“…Let the bend angle γ of the chain belong to [0; ω − π/3). The continuous spectrum has band structure and is given by Equation (8). There are eigenvalues of infinite multiplicity which are given by the eigenvalues of the Neumann Laplacian for the ball corresponding to the eigenfunctions vanishing at the both opposite points of the ball (x j and x j−1 ).…”

Section: Resultsmentioning

confidence: 99%

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Zigzag chain model and its spectrum

Melikhova¹

2017

Nanosystems: Phys. Chem. Math.

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This work describes the development of a model using a zigzag chain of weakly-coupled ball resonators with Neumann boundary conditions. The chain is assumed to be constructed of identical resonators connected through point-like apertures. The connecting points are described by their delta-coupling with a constant intensity. The model is based on the theory of self-adjoint extensions of symmetrical operators. Due to effectively one-dimensional joints, the 3D problem can be solved with assistance from the transfer matrix approach. This allows us to study the spectrum of the physical system. In particular, it is proven that the discrete spectrum of direct zigzag chain is empty while bending deformation leads to the appearance of non-empty discrete spectrum. In addition, the continuous spectrum has band structure. With the help of asymptotic study, we obtain the dependence of the spectrum structure on the geometrical and physical parameters of the system: zigzag angle, bend angle and coupling intensity.

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Section: Resultsmentioning

confidence: 99%

“…Two-dimensional resonators are in the focus of the papers [4][5][6], which studies spectral problems of direct and zigzag-like chains of disks, and bent chain of nanospheres respectively. Finally, chains consisting of three-dimensional resonators are presented in [7][8][9].…”

Section: Introductionmentioning

confidence: 99%

Zigzag chain model and its spectrum

Melikhova¹

2017

Nanosystems: Phys. Chem. Math.

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show abstract

Estimates for numbers of negative eigenvalues of Laplacian for Y-type chain of weakly coupled ball resonators

Cited by 1 publication

References 6 publications

Zigzag chain model and its spectrum

Zigzag chain model and its spectrum

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