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Вид документа : Статья из журнала
Шифр издания :
Автор(ы) : Rotter I., Sadreev A. F.
Заглавие : Singularities caused by coalesced complex eigenvalues of an effective hamilton operator
Разночтения заглавия :авие SCOPUS: Singularities caused by coalesced complex eigenvalues of an effective Hamilton operator
Место публикации : Int. J. Theor. Phys.: SPRINGER/PLENUM PUBLISHERS, 2007. - Vol. 46: 25th International Colloquium on Group Theoretical Methods in Physics (AUG 02-06, 2004, Cocoyoc, MEXICO), Is. 8. - P1914-1928. - ISSN 0020-7748, DOI 10.1007/s10773-006-9328-4
Примечания : Cited References: 38
Предметные рубрики: UNIMOLECULAR REACTION-RATES
EXCEPTIONAL POINTS
OVERLAPPING RESONANCES
NUCLEAR REACTIONS
QUANTUM-SYSTEMS
UNIFIED THEORY
S-MATRIX
CONTINUUM
PHASE
DEGENERACY
Ключевые слова (''Своб.индексиров.''): effective hamilton--complex eigenvalue--quantum dots--branch points--branch points--complex eigenvalue--effective hamilton--quantum dots
Аннотация: The S matrix theory with use of the effective Hamiltonian is sketched and applied to the description of the transmission through double quantum dots. The effective Hamilton operator is non-hermitian, its eigenvalues are complex, the eigenfunctions are bi-orthogonal. In this theory, singularities occur at points where two (or more) eigenvalues of the effective Hamiltonian coalesce. These points are physically meaningful: they separate the scenario of avoided level crossings from that without any crossings in the complex plane. They are branch points in the complex plane. Their geometrical features are different from those of the diabolic points.
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Вид документа : Статья из журнала
Шифр издания :
Автор(ы) : Sadreev A. F.
Заглавие : Interference traps waves in an open system: bound states in the continuum
Коллективы : Russian Foundation for Basic Research Projects [19-02-00055]
Место публикации : Rep. Prog. Phys. - 2021. - Vol. 84, Is. 5. - Ст.055901. - ISSN 0034-4885, DOI 10.1088/1361-6633/abefb9. - ISSN 1361-6633(eISSN)
Примечания : Cited References: 154. - The work was partially supported by Russian Foundation for Basic Research Projects No. 19-02-00055
Предметные рубрики: FANO RESONANCES
2ND-HARMONIC GENERATION
QUANTUM-SYSTEMS
UNIFIED THEORY
Аннотация: I review the four mechanisms of bound states in the continuum (BICs) in the application of microwave and acoustic cavities open to directional waveguides. The most simple are symmetry-protected BICs, which are localized inside the cavity because of the orthogonality of the eigenmodes to the propagating modes of waveguides. However, the most general and interesting is the Friedrich-Wintgen mechanism, when the BICs are the result of the fully destructive interference of outgoing resonant modes. The third type of BICs, Fabry-Perot BICs, occurs in a double resonator system when each resonator can serve as an ideal mirror. Finally, the accidental BICs can be realized in the open cavities with no symmetry like the open Sinai billiard in which the eigenmode of the resonator can become orthogonal to the continuum of the waveguide accidentally due to a smooth deformation of the eigenmode. We also review the one-dimensional systems in which the BICs occur owing to the fully destructive interference of two waves separated by spin or polarization or by paths in the Aharonov-Bohm rings. We make broad use of the method of effective non-Hermitian Hamiltonian equivalent to the coupled mode theory, which detects BICs by finding zero-width resonances.
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