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Rotter, I.
Singularities caused by coalesced complex eigenvalues of an effective hamilton operator / I. . Rotter, A. F. Sadreev // Int. J. Theor. Phys. - 2007. - Vol. 46: 25th International Colloquium on Group Theoretical Methods in Physics (AUG 02-06, 2004, Cocoyoc, MEXICO), Is. 8. - P. 1914-1928, DOI 10.1007/s10773-006-9328-4. - Cited References: 38 . - ISSN 0020-7748

РУБ Physics, Multidisciplinary
Рубрики:
UNIMOLECULAR REACTION-RATES
   EXCEPTIONAL POINTS
   OVERLAPPING RESONANCES
   NUCLEAR REACTIONS
   QUANTUM-SYSTEMS
   UNIFIED THEORY
   S-MATRIX
   CONTINUUM
   PHASE
   DEGENERACY
Кл.слова (ненормированные):
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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Держатели документа:
Max Planck Inst Phys Komplexer Syst, D-01187 Dresden, Germany
LV Kirenskii Inst Phys, Krasnoyarsk 660036, Russia
Linkoping Univ, Dept Phys & Measurement Technol, S-58183 Linkoping, Sweden
ИФ СО РАН
Max-Planck-Institut fur Physik Komplexer Systeme, D-01187 Dresden, Germany
Kirensky Institute of Physics, Krasnoyarsk 660036, Russian Federation
Department of Physics and Measurement Technology, Linkoping University, S-58183 Linkoping, Sweden

Доп.точки доступа:
Sadreev, A. F.; Садреев, Алмаз Фаттахович
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Sadreev, A. F.
Interference traps waves in an open system: bound states in the continuum / A. F. Sadreev // Rep. Prog. Phys. - 2021. - Vol. 84, Is. 5. - Ст. 055901, DOI 10.1088/1361-6633/abefb9. - Cited References: 154. - The work was partially supported by Russian Foundation for Basic Research Projects No. 19-02-00055 . - ISSN 0034-4885. - ISSN 1361-6633

РУБ Physics, Multidisciplinary
Рубрики:
FANO RESONANCES
   2ND-HARMONIC GENERATION
   QUANTUM-SYSTEMS
   UNIFIED THEORY
Кл.слова (ненормированные):
bound states in the continuum -- wave localization in one-dimensional wires -- open microwave and acoustic resonators -- effective non Hermitian Hamiltonian
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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Держатели документа:
Fed Res Ctr KSC SB RAS, Kirensky Inst Phys, Krasnoyarsk 660036, Russia.

Доп.точки доступа:
Садреев, Алмаз Фаттахович; Russian Foundation for Basic Research Projects [19-02-00055]
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