Spectral problem for solvable model of bent nano peapod

Abstract

The spectral problems for straight and bent chains of weakly coupled conglobate resonators are considered. The band structure of the continuous spectrum is described for the system of straight-type chain. For the bent chain, it is proved that the Hamiltonian has negative eigenvalue for some value of the model parameters and eigenvalues in gaps of the continuous spectrum.

Keywords:

• Spectrum
• theory of extensions
• self-adjoint operator
• transfer-matrix

AMS Subject Classifications:

• 81Q10
• 81Q35

Notes

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was partially financially supported by the Government of the Russian Federation [grant number 074-U01]; the Ministry of Science and Education of the Russian Federation [GOSZADANIE 2014/190, Project 14.Z50.31.0031]; President of the Russian Federation [grant number MK-5001.2015.1].