Spectral problem for solvable model of bent nano peapod

Mathematical model of weakly coupled spherical resonator chains under the influence of external magnetic field

“…A mathematical model of interacting resonators is constructed within the framework of the theory of self-adjoint extensions of symmetric operators [17]. The scheme for constructing a model of interacting resonators under the influence of an external magnetic field is similar to that in [3].…”

“…It is named due to their resemblance to the seedpod of the pea plant. There are a number of works dealing with mathematical modelling of mechanical, optical and electronic properties of nano-peapods [2][3][4][5]. Since the properties of carbon peapods differ from those of nanotubes and fullerenes, the carbon peapod can be recognized as a new type of a self-assembled graphitic structure [6].…”

“…Possible applications of nano-peapods include nanoscale lasers, single electron transistors, spin-qubit arrays for quantum computing, nanopipettes, and data storage devices thanks to the memory effects and superconductivity of nano-peapods [7][8][9][10]. Spectral problems for a chain of coupled resonator attract a special interest due to its usefulness for micro and nanoelectronics, radio physics, acoustics [3,11,12].…”

Photon generation in resonator with time dependent boundary conditions

“…Results of applying numerical schemes to these problems may be found in [14,15]. Consideration of topologically nontrivial structures for realization DCE requires a number of simple analytical models for a chain of one-dimensional connected resonators with different couplings [16,17,19,[23][24][25]. Here, formalism of quantum graphs is widely used [20,26,27].…”

Zigzag chain model and its spectrum

“…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].…”