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Bulgakov, E. N.
Bound states in photonic Fabry-Perot resonator with nonlinear off-channel defects / E. N. Bulgakov, A. F. Sadreev // Phys. Rev. B. - 2010. - Vol. 81, Is. 11. - Ст. 115128, DOI 10.1103/PhysRevB.81.115128. - Cited References: 73. - The work was partially supported by RFBR under Grant No. 09-02-98005 "Siberia." We are greatly acknowledge Konstantin Pichugin for many discussions. . - ISSN 1098-0121

РУБ Physics, Condensed Matter
Рубрики:
CRYSTAL WAVE-GUIDES
   STATIONARY LOCALIZED STATES
   COUPLED-MODE THEORY
   OPTICAL RESONATORS
   NUCLEAR REACTIONS
   UNIFIED THEORY
   MICROCAVITIES
   TRANSMISSION
   CONTINUUM
   CIRCUITS
Аннотация: We consider a Fabry-Perot resonator (FPR) comprised of two off-channel nonlinear defects coupled to the photonic waveguide. For the linear case FPR can support bound states in the form of standing waves between the defects if a distance between them is quantized. For the nonlinear case the bound states appear for arbitrary distance between the defects if electromagnetic intensity is quantized. For transmission through the FPR we reveal additional resonances which are the result of coupling of incident wave with the bound states because of nonlinearity of the defects. The resonances are spaced at the eigenfrequencies of bound states with a width proportional to the input amplitude. The theory of the FPR based on the simple Wang and Fan model [Phys. Rev. E 68, 066616 (2003)] is complemented by the tight-binding one. The results for the transmission and bound states in these models agree with computations in real two-dimensional photonic crystal waveguide coupled with two off-channel defects fabricated from a Kerr-type material.

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Держатели документа:
[Bulgakov, Evgeny N.
Sadreev, Almas F.] Russian Acad Sci, Inst Phys, Krasnoyarsk 660036, Russia
[Bulgakov, Evgeny N.] Siberian State Aerosp Univ, Krasnoyarsk, Russia
ИФ СО РАН
Institute of Physics, Academy of Sciences, 660036 Krasnoyarsk, Russian Federation
Siberian State Aerospace University, Krasnoyarsk Rabochii, 31, Krasnoyarsk, Russian Federation

Доп.точки доступа:
Sadreev, A. F.; Садреев, Алмаз Фаттахович; Булгаков, Евгений Николаевич
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Bulgakov, E. N.
Correlated behavior of conductance and phase rigidity in the transition from the weak-coupling to the strong-coupling regime / E. N. Bulgakov, I. . Rotter, A. F. Sadreev // Phys. Rev. B. - 2007. - Vol. 76, Is. 21. - Ст. 214302, DOI 10.1103/PhysRevB.76.214302. - Cited References: 42 . - ISSN 1098-0121

РУБ Physics, Condensed Matter
Рубрики:
OPEN QUANTUM-SYSTEMS
   NUCLEAR CROSS-SECTIONS
   UNIFIED THEORY
   FLUCTUATIONS
   CONTINUUM
   BILLIARD
   STATES
Аннотация: We study the transmission through different small systems as a function of the coupling strength v to the two attached leads. The leads are identical with only one propagating mode xi(E)(C) in each of them. In addition to the conductance G, we calculate the phase rigidity rho of the scattering wave function Psi(E)(C) in the interior of the system. Most interesting results are obtained in the regime of strongly overlapping resonance states where the crossover from staying to traveling modes takes place. The crossover is characterized by collective effects. Here, the conductance is plateaulike enhanced in some energy regions of finite length while corridors with zero transmission (total reflection) appear in other energy regions. This transmission picture depends only weakly on the spectrum of the closed system. It is caused by the alignment of some resonance states of the system with the propagating modes xi(E)(C) in the leads. The alignment of resonance states takes place stepwise by resonance trapping, i.e., it is accompanied by the decoupling of other resonance states from the continuum of propagating modes. This process is quantitatively described by the phase rigidity rho of the scattering wave function. Averaged over energy in the considered energy window, G is correlated with 1-rho . In the regime of strong coupling, only two short-lived resonance states survive each aligned with one of the channel wave functions xi(E)(C). They may be identified with traveling modes through the system. The remaining M-2 trapped narrow resonance states are well separated from one another.

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Держатели документа:
[Bulgakov, E. N.
Rotter, I.
Sadreev, A. F.] Max Planck Inst Phys Komplexer Syst, D-01187 Dresden, Germany
[Bulgakov, E. N.
Sadreev, A. F.] LV Kirenskii Inst Phys, Krasnoyarsk 660036, Russia
ИФ СО РАН
Max Planck Institute for the Physics of Complex Systems, D-01187 Dresden, Germany
Kirensky Institute of Physics, 660036, Krasnoyarsk, Russian Federation

Доп.точки доступа:
Rotter, I.; Sadreev, A. F.; Садреев, Алмаз Фаттахович; Булгаков, Евгений Николаевич
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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.
S-matrix formalism of transmission through two quantum billiards coupled by a waveguide / A. F. Sadreev, E. N. Bulgakov, I. . Rotter // J. Phys. A. - 2005. - Vol. 38, Is. 49. - P. 10647-10661, DOI 10.1088/0305-4470/38/49/012. - Cited References: 32 . - ISSN 0305-4470

РУБ Physics, Multidisciplinary + Physics, Mathematical
Рубрики:
CIRCULAR BENDS
   DOTS
   TRANSPORT
   CONTINUUM
   SYSTEMS
   STATES
Аннотация: We consider a system that consists of two single-quantum billiards (QBs) coupled by a waveguide and study the transmission through this system as a function of length and width of the waveguide. To interpret the numerical results for the transmission, we explore a simple model with a small number of states which allows us to consider the problem analytically. The transmission is described in the S-matrix formalism by using the non-Hermitian effective Hamilton operator for the open system. The coupling of the single QBs to the internal waveguide characterizes the 'internal' coupling strength u of the states of the system while that of the system as a whole to the attached leads determines the 'external' coupling strength v of the resonance states via the continuum (waves in the leads). The transmission is resonant for all values of v/u in relation to the effective Hamiltonian. It depends strongly on the ratio u/u via the eigenvalues and eigenfunctions of the effective Hamiltonian. The results obtained are compared qualitatively with those from simulation calculations for larger systems. Most interesting is the existence of resonance states with vanishing widths that may appear at all values of v/u. They cause zeros in the transmission through the double QB due to trapping of the particle in the waveguide.

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Держатели документа:
LV Kirenskii Inst Phys, Krasnoyarsk 660036, Russia
Linkoping Univ, Dept Phys & Measurement Technol, S-58183 Linkoping, Sweden
Max Planck Inst Phys Komplexer Syst, D-01187 Dresden, Germany
ИФ СО РАН
Kirensky Institute of Physics, Krasnoyarsk, 660036, Russian Federation
Department of Physics and Measurement Technology, Linkoping University, S-581 83 Linkoping, Sweden
Max-Planck-Institut fur Physik Komplexer Systeme, D-01187 Dresden, Germany

Доп.точки доступа:
Bulgakov, E. N.; Булгаков, Евгений Николаевич; Rotter, I.; Садреев, Алмаз Фаттахович
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Rotter, I.
Avoided level crossings, diabolic points, and branch points in the complex plane in an open double quantum dot / I. . Rotter, A. F. Sadreev // Phys. Rev. E. - 2005. - Vol. 71, Is. 3. - Ст. 36227, DOI 10.1103/PhysRevE.71.036227. - Cited References: 49 . - ISSN 1063-651X

РУБ Physics, Fluids & Plasmas + Physics, Mathematical
Рубрики:
BERRY TOPOLOGICAL PHASE
   EXCEPTIONAL POINTS
   GEOMETRIC PHASES
   NUCLEAR REACTIONS
   RESONANCE STATES
   UNIFIED THEORY
   S-MATRIX
   CONTINUUM
   REPULSION
   INTERFEROMETER
Кл.слова (ненормированные):
Branch points in the complex plane (BPCP) -- Diabolic points (DP) -- Geometric phases -- Riemann sheets -- Eigenvalues and eigenfunctions -- Electron energy levels -- Functions -- Hamiltonians -- Quantum theory -- Resonance -- Topology -- Semiconductor quantum dots
Аннотация: We study the spectrum of an open double quantum dot as a function of different system parameters in order to receive information on the geometric phases of branch points in the complex plane (BPCP). We relate them to the geometrical phases of the diabolic points (DPs) of the corresponding closed system. The double dot consists of two single dots and a wire connecting them. The two dots and the wire are represented by only a single state each. The spectroscopic values follow from the eigenvalues and eigenfunctions of the Hamiltonian describing the double dot system. They are real when the system is closed, and complex when the system is opened by attaching leads to it. The discrete states as well as the narrow resonance states avoid crossing. The DPs are points within the avoided level crossing scenario of discrete states. At the BPCP, width bifurcation occurs. Here, different Riemann sheets evolve and the levels do not cross anymore. The BPCP are physically meaningful. The DPs are unfolded into two BPCP with different chirality when the system is opened. The geometric phase that arises by encircling the DP in the real plane, is different from the phase that appears by encircling the BPCP. This is found to be true even for a weakly opened system and the two BPCP into which the DP is unfolded.

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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
Astafev Krasnoyarsk Pedag Univ, Krasnoyarsk 660049, Russia
ИФ СО РАН
Max-Planck-Inst. Physik Komplexer S., D-01187 Dresden, Germany
Kirensky Institute of Physics, 660036, Krasnoyarsk, Russian Federation
Dept. of Physics and Measurement, Technology Linkoping University, S-581 83 Linkoping, Sweden
Astafev Krasnoyarsk Pedagogical U., 660049 Krasnoyarsk, Russian Federation

Доп.точки доступа:
Sadreev, A. F.; Садреев, Алмаз Фаттахович
}
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Rotter, I.
Influence of branch points in the complex plane on the transmission through double quantum dots / I. . Rotter, A. F. Sadreev // Phys. Rev. E. - 2004. - Vol. 69, Is. 6. - Ст. 66201, DOI 10.1103/PhysRevE.69.066201. - Cited References: 25 . - ISSN 1539-3755

РУБ Physics, Fluids & Plasmas + Physics, Mathematical
Рубрики:
ELECTRON-ATOM SCATTERING
   S-MATRIX
   DOUBLE POLES
   CONTINUUM
   SYSTEM
   MODEL
Кл.слова (ненормированные):
Eigenvalues and eigenfunctions -- Hamiltonians -- Mathematical models -- Matrix algebra -- Probability -- Resonance -- Scattering -- Wave propagation -- Branch points -- Open quantum systems -- Propagating modes -- Quantum computing devices -- Semiconductor quantum dots
Аннотация: We consider single-channel transmission through a double quantum dot system consisting of two single dots that are connected by a wire and coupled each to one lead. The system is described in the framework of the S matrix theory by using the effective Hamiltonian of the open quantum system. It consists of the Hamiltonian of the closed system (without attached leads) and a term that accounts for the coupling of the states via the continuum of propagating modes in the leads. This model allows one to study the physical meaning of branch points in the complex plane. They are points of coalesced eigenvalues and separate the two scenarios with avoided level crossings and without any crossings in the complex plane. They influence strongly the features of transmission through double quantum dots.

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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, S-58183 Linkoping, Sweden
Astafev Kransnoyarsk Pedag Univ, Krasnoyarsk 660049, Russia
ИФ СО РАН
Max-Planck-Inst. Phys. Komplexer S., D-01187 Dresden, Germany
Kirensky Institute of Physics, Krasnoyarsk, 660036, Russian Federation
Department of Physics, Linkoping University, S-581 83 Linkoping, Sweden
Astaf'ev Krasnoyarsk Pedagogical U., 89 Lebedeva, Krasnoyarsk, 660049, Russian Federation

Доп.точки доступа:
Sadreev, A. F.; Садреев, Алмаз Фаттахович
}
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Bulgakov, E. N.
Phase rigidity and avoided level crossings in the complex energy plane / E. N. Bulgakov, I. . Rotter, A. F. Sadreev // Phys. Rev. E. - 2006. - Vol. 74, Is. 5. - Ст. 56204, DOI 10.1103/PhysRevE.74.056204. - Cited References: 40 . - ISSN 1539-3755

РУБ Physics, Fluids & Plasmas + Physics, Mathematical
Рубрики:
OPEN QUANTUM-SYSTEMS
   FANO RESONANCES
   S-MATRIX
   DOT
   CONTINUUM
   TRANSMISSION
   COHERENCE
   TRANSPORT
   BILLIARDS
   PROBE
Кл.слова (ненормированные):
Eigenvalues and eigenfunctions -- Hamiltonians -- Resonance -- Rigidity -- Semiconductor quantum dots -- Biorthogonal eigenfunctions -- Open quantum system -- Phase rigidity -- Quantum theory
Аннотация: We consider the effective Hamiltonian of an open quantum system, its biorthogonal eigenfunctions phi(lambda), and define the value r(lambda)=(phi(lambda)parallel to phi(lambda))/ that characterizes the phase rigidity of the eigenfunctions phi(lambda). In the scenario with avoided level crossings, r(lambda) varies between 1 and 0 due to the mutual influence of neighboring resonances. The variation of r(lambda) is an internal property of an open quantum system. In the literature, the phase rigidity rho of the scattering wave function Psi(E)(C) is considered. Since Psi(E)(C) can be represented in the interior of the system by the phi(lambda), the phase rigidity rho of the Psi(E)(C) is related to the r(lambda) and therefore also to the mutual influence of neighboring resonances. As a consequence, the reduction of the phase rigidity rho to values smaller than 1 should be considered, at least partly, as an internal property of an open quantum system in the overlapping regime. The relation to measurable values such as the transmission through a quantum dot, follows from the fact that the transmission is, in any case, resonant at energies that are determined by the real part of the eigenvalues of the effective Hamiltonian. We illustrate the relation between phase rigidity rho and transmission numerically for small open cavities.

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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, 660036 Krasnoyarsk, Russian Federation
Department of Physics and Measurement, Technology Linkoping University, S-581 83 Linkoping, Sweden

Доп.точки доступа:
Rotter, I.; Sadreev, A. F.; Садреев, Алмаз Фаттахович; Булгаков, Евгений Николаевич
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Bulgakov, E. N.
Bound States in Photonic Fabry-Perot Resonator Comprised of Two Nonlinear Off-Channel Defects / E. N. Bulgakov, A. F. Sadreev // JETP Letters. - 2009. - Vol. 90, Is. 12. - P. 744-749, DOI 10.1134/S0021364009240023. - Cited References: 32. - We thank Kostya Pichugin for many helpful discussions. The work was partially supported by the Russian Foundation for Basic Research, project no. 09-02-98005-Siberia. . - ISSN 0021-3640

РУБ Physics, Multidisciplinary
Рубрики:
SCATTERING-THEORY
   WAVE-GUIDE
   CONTINUUM
   MODES
Аннотация: Two off-channel nonlinear defects coupled to the photonic waveguide constitute the Fabry-Perot interfer-ometer (FPR). The defects are made from a Kerr-like nonlinear material. For the linear case such a FPR can support the bound states in the form of standing waves between the defects if the distance between them is quantized. For the nonlinear case the bound states appear for arbitrary distance between the defects however for an quantized electromagnetic intensity. For the transmission through FPR we reveal new resonances and show these are a result of coupling of the bound states with incident wave because of nonlinearity of the defects. The resonances are spaced at the eigen frequencies of bound states.

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Держатели документа:
[Bulgakov, E. N.
Sadreev, A. F.] Russian Acad Sci, Inst Phys, Krasnoyarsk 660036, Russia
[Bulgakov, E. N.] Siberian State Aerosp Univ, Krasnoyarsk, Russia
ИФ СО РАН
Institute of Physics, Academy of Sciences, Krasnoyarsk 660036, Russian Federation
Siberian State Aerospace University, Krasnoyarsk, Russian Federation

Доп.точки доступа:
Sadreev, A. F.; Садреев, Алмаз Фаттахович; Булгаков, Евгений Николаевич; Russian Foundation for Basic Research [09-02-98005-Siberia]
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Bulgakov, E. N.
Propagating Bloch bound states with orbital angular momentum above the light line in the array of dielectric spheres / E. N. Bulgakov, A. F. Sadreev // J. Opt. Soc. Am. A. - 2017. - Vol. 34, Is. 6. - P. 949-952, DOI 10.1364/JOSAA.34.000949. - Cited References:37. - Ministry of Education and Science of the Russian Federation (Minobrnauka) (N 3.1845.2017); Russian Foundation for Basic Research (RFBR) (16-02-00314). . - ISSN 1084-7529. - ISSN 1520-8532

РУБ Optics
Рубрики:
GUIDED-WAVES
   CONTINUUM
   BEHAVIOR
   GRATINGS
Аннотация: We present propagating Bloch bound states in the radiation continuum with orbital angular momentum in an infinite linear periodical array of dielectric spheres. The bound states in the continuum demonstrate a giant Poynting vector spiraling around the array. They can be excited by a plane wave with incident linear polarization with a small tilt relative to the axis of the array.

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Держатели документа:
RAS, Kirensky Inst Phys, Fed Res Ctr, KSC,SB, Krasnoyarsk 660036, Russia.
Siberian State Aerosp Univ, Krasnoyarsk, Russia.

Доп.точки доступа:
Sadreev, A. F.; Садреев, Алмаз Фаттахович; Булгаков, Евгений Николаевич; Ministry of Education and Science of the Russian Federation (Minobrnauka) [N 3.1845.2017]; Russian Foundation for Basic Research (RFBR) [16-02-00314]
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10.

Bulgakov, E. N.
Scattering plane waves by a dielectric cylinder with periodically modulated permittivity at oblique incidence / E. N. Bulgakov, A. F. Sadreev // Phys. Rev. A. - 2018. - Vol. 97, Is. 6. - Ст. 063856, DOI 10.1103/PhysRevA.97.063856. - Cited References: 24. - We acknowledge discussions with A. A. Bogdanov and D. N. Maksimov. This paper was partially supported by Ministry of Education and Science of Russian Federation (State Contract No. 3.1845.2017) and Russian Foundation for Basic Research Grant No. 16-02-00314. . - ISSN 2469-9926. - ISSN 2469-9934

РУБ Optics + Physics, Atomic, Molecular & Chemical
Рубрики:
BOUND-STATES
   FANO RESONANCE
   LIGHT LINE
   CONTINUUM
   ARRAYS
Аннотация: For scattering of electromagnetic waves by a dielectric cylinder with periodically modulated permittivity we focus on the vicinity of the frequency of the wave with regard to the eigenfrequencies of bound states in the continuum. Then response of the cylinder becomes extremely sensitive to the angle of incidence and polarization of the plane wave. The cross section of the scattering of electromagnetic waves with mixed polarization undergoes crucial change from the Bragg shape to the Fano shape by rotation of the polarization that paves a way to tuning of Fano resonances by an external source.

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Держатели документа:
RAS, Fed Res Ctr KSC SB, Kirensky Inst Phys, Krasnoyarsk 660036, Russia.
Siberian State Aerosp Univ, Krasnoyarsk 660014, Russia.

Доп.точки доступа:
Sadreev, A. F.; Садреев, Алмаз Фаттахович; Булгаков, Евгений Николаевич; Ministry of Education and Science of Russian Federation [3.1845.2017]; Russian Foundation for Basic Research [16-02-00314]
}
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