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Voltage-induced defect mode coupling in a one-dimensional photonic crystal with a twisted-nematic defect layer / I. V. Timofeev [et al.] // Phys. Rev. E. - 2012. - Vol. 85, Is. 1. - Ст. 11705, DOI 10.1103/PhysRevE.85.011705. - Cited References: 39. - This work was supported in part by DSP Grant No. 2.1.1/3455; RAS Grants No. 3.9.1 and No. 21.1, SB RAS Grants No. 5 and No. 144, and by the National Science Council of Taiwan under Grant No. NSC 98-2923-M-033-001-MY3. . - ISSN 1539-3755

РУБ Physics, Fluids & Plasmas + Physics, Mathematical
Рубрики:
LIQUID-CRYSTAL
   REFLECTION SPECTRUM
   OPTICAL-PROPERTIES
   ANISOTROPIC MEDIA
   ELECTRIC-FIELD
   EIGENVALUES
   ORIENTATION
Аннотация: Defect modes are investigated in a band gap of an electrically tunable one-dimensional photonic crystal infiltrated with a twisted-nematic liquid crystal. Their frequency shift and interference under applied voltage are studied both experimentally and theoretically. We deal with the case where the defect layer thickness is much larger than the wavelength (i.e., the Mauguin condition). It is shown theoretically that the defect modes could have a complex structure with elliptic polarization. Two series of polarized modes are coupled with each other and exhibit an avoided crossing phenomenon in the case of opposite parity.

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Держатели документа:
[Timofeev, Ivan V.
Gunyakov, V. A.
Myslivets, Sergey A.
Arkhipkin, V. G.
Zyryanov, Victor Ya] Russian Acad Sci, Krasnoyarsk Sci Ctr, LV Kirensky Phys Inst, Siberian Branch, Krasnoyarsk 660036, Russia
[Timofeev, Ivan V.
Gunyakov, Vladimir A.
Arkhipkin, V/ G.
Vetrov, Stepan Ya] Siberian Fed Univ, Krasnoyarsk 660041, Russia
[Lin, Yu-Ting] Chung Yuan Christian Univ, Master Program Nanotechnol, Chungli 32023, Taiwan
[Lee, Wei] Chung Yuan Christian Univ, Dept Phys, Chungli 32023, Taiwan
[Lee, Wei] Chung Yuan Christian Univ, Ctr Nanotechnol, Chungli 32023, Taiwan
[Zyryanov, Victor Ya] Siberian State Aerosp Univ, Krasnoyarsk 660014, Russia

Доп.точки доступа:
Timofeev, I. V.; Тимофеев, Иван Владимирович; Lin, Y. T.; Gunyakov, V. A.; Гуняков, Владимир Алексеевич; Myslivets, S. A.; Мысливец, Сергей Александрович; Arkhipkin, V. G.; Архипкин, Василий Григорьевич; Vetrov, S. Y.; Lee, W.; Zyryanov, V. Ya.; Зырянов, Виктор Яковлевич
}
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Nikolaev, S. V.
Cluster perturbation theory in Hubbard model exactly taking into account the short-range magnetic order in 2 x 2 cluster / S. V. Nikolaev, S. G. Ovchinnikov // J. Exp. Theor. Phys. - 2010. - Vol. 111, Is. 4. - P. 635-644, DOI 10.1134/S1063776110100146. - Cited References: 23. - The authors thank V. V. Val'kov for fruitful discussions of this work. This research was supported financially by the Russian Foundation for Basic Research (project nos. 09-02-90723-mob_st and 09-02-00127) and by program no. 5.7 of the Presidium of the Russian Academy of Sciences and integration project no. 40 of the Siberian Branch and Ural Division of the Russian Academy of Sciences. . - ISSN 1063-7761

РУБ Physics, Multidisciplinary
Рубрики:
INFINITE DIMENSIONS
SYSTEMS
STATE
Кл.слова (ненормированные):
Antiferromagnetic orders -- Characteristic energy -- Cluster perturbation theories -- Coulomb repulsions -- Density of state -- Dynamic mean field theories -- Eigenvalue problem -- Exact diagonalization -- Excited levels -- Finite temperatures -- Half-filling -- Hubbard -- Metal insulator transition temperature -- Nearest neighbors -- Numerical solution -- Pseudo-gap -- Quasiparticle spectrum -- Shadow zone -- Short-range magnetic orders -- Temperature evolution -- Zero temperatures -- Antiferromagnetism -- Eigenvalues and eigenfunctions -- Fermi level -- Hubbard model -- Mean field theory -- Metal insulator boundaries -- Perturbation techniques -- Semiconductor insulator boundaries -- Statistical mechanics -- Metal insulator transition
Аннотация: The cluster perturbation theory is presented in the 2D Hubbard model constructed using X operators in the Hubbard-I approximation. The short-range magnetic order is taken into account by dividing the entire lattice into individual 2 x 2 clusters and solving the eigenvalue problem in an individual cluster using exact diagonalization taking into account all excited levels. The case of half-filling taking into account jumps between nearest neighbors is considered. As a result of numerical solution, a shadow zone is discovered in the quasiparticle spectrum. It is also found that a gap in the density of states in the quasiparticle spectrum at zero temperature exists for indefinitely small values of Coulomb repulsion parameter U and increases with this parameter. It is found that the presence of this gap in the spectrum is due to the formation of a short-range antiferromagnetic order. An analysis of the temperature evolution of the density of states shows that the metal-insulator transition occurs continuously. The existence of two characteristic energy scales at finite temperatures is demonstrated, the larger scale is associated with the formation of a pseudogap in the vicinity of the Fermi level, and the smaller scale is associated with the metal-insulator transition temperature. A peak in the density of states at the Fermi level, which is predicted in the dynamic mean field theory in the vicinity of the metal-insulator transition, is not observed.

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Держатели документа:
[Nikolaev, S. V.
Ovchinnikov, S. G.] Russian Acad Sci, Kirenskii Inst Phys, Siberian Branch, Krasnoyarsk 660036, Russia
[Nikolaev, S. V.] Dostoevsky State Univ, Omsk 644077, Russia
[Ovchinnikov, S. G.] Siberian Fed Univ, Krasnoyarsk 660041, Russia
ИФ СО РАН
Kirenskii Institute of Physics, Siberian Branch, Russian Academy of Sciences, Krasnoyarsk 660036, Russian Federation
Dostoevsky State University, Omsk 644077, Russian Federation
Siberian Federal University, Krasnoyarsk 660041, Russian Federation

Доп.точки доступа:
Ovchinnikov, S. G.; Овчинников, Сергей Геннадьевич
}
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Nesterov, A. I.
Geometric phases and quantum phase transitions in open systems / A. I. Nesterov, S. G. Ovchinnikov // Phys. Rev. E. - 2008. - Vol. 78, Is. 1. - Ст. 15202, DOI 10.1103/PhysRevE.78.015202. - Cited References: 29 . - ISSN 1539-3755

РУБ Physics, Fluids & Plasmas + Physics, Mathematical
Рубрики:
POINTS
DEGENERACIES
Кл.слова (ненормированные):
Chlorine compounds -- Electron tunneling -- Ferromagnetism -- Ising model -- Magnetic fields -- Magnetism -- Open systems -- Quantum electronics -- Quantum optics -- Sedimentation -- Effective Hamiltonian -- Eigenvalues -- First orders -- Geometric phase -- Geometric phases -- Ground-state -- Hermitian -- One-dimensional -- Open quantum systems -- Quantum phase transition -- Quantum phase transitions -- Transverse-magnetic fields -- Phase transitions
Аннотация: The relationship is established between quantum phase transitions and complex geometric phases for open quantum systems governed by a non-Hermitian effective Hamiltonian with accidental crossing of the eigenvalues. In particular, the geometric phase associated with the ground state of the one-dimensional dissipative Ising model in a transverse magnetic field is evaluated, and it is demonstrated that the related quantum phase transition is of the first order.

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Держатели документа:
[Nesterov, Alexander I.] Univ Guadalajara, CUCEI, Dept Fis, Guadalajara 44420, Jalisco, Mexico
[Ovchinnikov, S. G.] SB RAS, LV Kirensky Phys Inst, Krasnoyarsk 660036, Russia
[Ovchinnikov, S. G.] Siberian Fed Univ, Krasnoyarsk 660041, Russia
ИФ СО РАН
Departamento de Fisica, CUCEI, Universidad de Guadalajara, Av. Revolucion 1500, Guadalajara, Codigo Postal 44420, Jalisco, Mexico
L. V. Kirensky Institute of Physics, SB, RAS, 660036 Krasnoyarsk, Russian Federation
Siberian Federal University, 660041, Krasnoyarsk, Russian Federation

Доп.точки доступа:
Ovchinnikov, S. G.; Овчинников, Сергей Геннадьевич
}
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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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Bulgakov, E. N.
Electric circuit networks equivalent to chaotic quantum billiards / E. N. Bulgakov, D. N. Maksimov, A. F. Sadreev // Phys. Rev. E. - 2005. - Vol. 71, Is. 4. - Ст. 46205, DOI 10.1103/PhysRevE.71.046205. - Cited References: 31 . - ISSN 1063-651X

РУБ Physics, Fluids & Plasmas + Physics, Mathematical
Рубрики:
TIME-REVERSAL SYMMETRY
   CONDUCTANCE FLUCTUATIONS
   STATISTICS
   SYSTEMS
   EIGENFUNCTIONS
   DOTS
Кл.слова (ненормированные):
Chaotic quantum billiards -- Electric resonance circuits (ERC) -- Resonance networks -- Wave functions -- Boundary conditions -- Capacitors -- Chaos theory -- Eigenvalues and eigenfunctions -- Electric inductors -- Natural frequencies -- Quantum theory -- Resonance -- Statistical mechanics -- Networks (circuits)
Аннотация: We consider two electric RLC resonance networks that are equivalent to quantum billiards. In a network of inductors grounded by capacitors, the eigenvalues of the quantum billiard correspond to the squared resonant frequencies. In a network of capacitors grounded by inductors, the eigenvalues of the billiard are given by the inverse of the squared resonant frequencies. In both cases, the local voltages play the role of the wave function of the quantum billiard. However, unlike for quantum billiards, there is a heat power because of the resistance of the inductors. In the equivalent chaotic billiards, we derive a distribution of the heat power which describes well the numerical statistics.

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Держатели документа:
LV Kirenskii Inst Phys, Krasnoyarsk 660036, Russia
Linkoping Univ, Dept Phys & Measurement Technol, S-58183 Linkoping, Sweden
Astafev Pedag Univ, Krasnoyarsk 660049, Russia
ИФ СО РАН
Kirensky Institute of Physics, 660036 Krasnoyarsk, Russian Federation
Dept. of Physics and Measurement, Technology Linkoping University, 5-557 83 Linkoping, Sweden
Astaf'Ev Pedagogical University, 89, Krasnoyarsk, 660049 Lebedeva, Russian Federation

Доп.точки доступа:
Maksimov, D. N.; Максимов, Дмитрий Николаевич; Sadreev, A. F.; Садреев, Алмаз Фаттахович; Булгаков, Евгений Николаевич
}
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Rotter, I.
Zeros in single-channel transmission through double quantum dots / I. . Rotter, A. F. Sadreev // Phys. Rev. E. - 2005. - Vol. 71, Is. 4. - Ст. 46204, DOI 10.1103/PhysRevE.71.046204. - Cited References: 28 . - ISSN 1063-651X

РУБ Physics, Fluids & Plasmas + Physics, Mathematical
Рубрики:
PHASE EVOLUTION
   RESONANCE
   TRANSPORT
   SYSTEMS
Кл.слова (ненормированные):
Fano interference -- Fano resonances -- Overlapping resonances -- Transmission amplitude -- Channel capacity -- Eigenvalues and eigenfunctions -- Function evaluation -- Hamiltonians -- Mathematical models -- Mathematical operators -- Matrix algebra -- Resonance -- Signal interference -- Semiconductor quantum dots
Аннотация: By using a simple model we consider single-channel transmission through a double quantum dot that consists of two single dots coupled by a wire of finite length L. Each of the two single dots is characterized by a few energy levels only, and the wire is assumed to have only one level whose energy depends on the length L. The transmission is described by using S matrix theory and the effective non-Hermitian Hamilton operator H-eff of the system. The decay widths of the eigenstates of H-eff depend strongly on energy. The model explains the origin of the transmission zeros of the double dot that is considered by us. Mostly, they are caused by (destructive) interferences between neighboring levels and are of first order. When, however, both single dots are identical and their transmission zeros are of first order, those of the double dot are of second order. First-order transmission zeros cause phase jumps of the transmission amplitude by pi, while there are no phase jumps related to second-order transmission zeros. In this latter case, a phase jump occurs due to the fact that the width of one of the states vanishes when crossing the energy of the transmission zero. The parameter dependence of the widths of the resonance states is determined by the spectral properties of the two single 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 Technol, S-58183 Linkoping, Sweden
Astafev Krasnoyarsk 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
Dept. of Phys. and Msrmt. Technology, Linkoping University, S-58183 Linkoping, Sweden
Astaf'ev Krasnoyarsk Pedagogical U., Krasnoyarsk, 660049, Russian Federation

Доп.точки доступа:
Sadreev, A. F.; 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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Bulgakov, E. N.
Statistics of wave functions and currents induced by spin-orbit interaction in chaotic billiards / E. N. Bulgakov, A. F. Sadreev // Phys. Rev. E. - 2004. - Vol. 70, Is. 5. - Ст. 56211, DOI 10.1103/PhysRevE.70.056211. - Cited References: 33 . - ISSN 1539-3755

РУБ Physics, Fluids & Plasmas + Physics, Mathematical
Рубрики:
HELMHOLTZ-EQUATION
   PERSISTENT CURRENTS
   ELECTRON-GAS
   RINGS
   EIGENFUNCTIONS
   SYSTEMS
   PHASE
Кл.слова (ненормированные):
Approximation theory -- Chaos theory -- Degrees of freedom (mechanics) -- Eigenvalues and eigenfunctions -- Electric field effects -- Electric potential -- Electron gas -- Hamiltonians -- Heterojunctions -- Microwaves -- Statistical methods -- Chaotic Robnik billiards -- Current distributions -- Spin-orbit interaction (SOI) -- Wave functions -- Quantum theory
Аннотация: We show that the wave function and current statistics in chaotic Robnik billiards crucially depend on the constant of the spin-orbit interaction (SOI). For small constant the current statistics is described by universal current distributions derived for slightly opened chaotic billiards [Saichev et al. J. Phys. A. 35, L87 (2002)] although one of the components of the spinor eigenfunctions is not universal. For strong SOI both components of the spinor eigenstate are complex random Gaussian fields. This observation allows us to derive the distributions of spin-orbit persistent cut-rents which well describe numerical statistics. For intermediate values of the statistics of the eigenstates and currents, both are deeply nonuniversal.

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Держатели документа:
LV Kirenskii Inst Phys, Krasnoyarsk 660036, Russia
Astafev Krasnoyarsk Pedag Univ, Lebedeva 660049 89, Russia
Linkoping Univ, IFM, S-58183 Linkoping, Sweden
ИФ СО РАН
Kirensky Institute of Physics, 660036, Krasnoyarsk, Russian Federation
Astaf'ev Krasnoyarsk Pedagogical U., 660049, Lebedeva, 89, Russian Federation
IFM, Linkoping University, S-581 83 Linkoping, Sweden

Доп.точки доступа:
Sadreev, A. F.; Садреев, Алмаз Фаттахович; Булгаков, Евгений Николаевич
}
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Sadreev, A. F.
Current statistics for transport through rectangular and circular billiards / A. F. Sadreev // Phys. Rev. E. - 2004. - Vol. 70, Is. 1. - Ст. 16208, DOI 10.1103/PhysRevE.70.016208. - Cited References: 21 . - ISSN 1539-3755

РУБ Physics, Fluids & Plasmas + Physics, Mathematical
Рубрики:
ELECTRON-TRANSPORT
   QUANTUM CHAOS
   NODAL POINTS
   RANDOM WAVES
   STREAMLINES
Кл.слова (ненормированные):
Bessel functions -- Current density -- Eigenvalues and eigenfunctions -- Electric potential -- Mathematical models -- Microwaves -- Parameter estimation -- Poisson distribution -- Probability -- Scattering -- Gaussian distribution -- Microwave transmission -- Resonant transmission -- Scattering functions -- Quantum theory
Аннотация: We consider the statistics of currents for electron (microwave) transmission through rectangular and circular billiards. For the resonant transmission the current distribution is describing by the universal distribution [ A. I. Saichev , J. Phys. A 35, L87 (2002) ]. For the more typical case of nonresonant transmission the current statistics reveals features of the current channeling (corridor effect) interior of the billiard. The numerical statistics is compared with analytical distributions.

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Держатели документа:
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
L.V. Kirensky Institute of Physics, Krasnoyarsk 660036, Russian Federation
Department of Physics, Linkoping University, S-581 83 Linkoping, Sweden
Astaf'ev Krasnoyarsk Pedagogical U., Krasnoyarsk 660049, Russian Federation

Доп.точки доступа:
Садреев, Алмаз Фаттахович
}
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10.

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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