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Berggren, K. F.
Crossover from regular to irregular behavior in current flow through open billiards / K. F. Berggren, A. F. Sadreev, A. A. Starikov // Phys. Rev. E. - 2002. - Vol. 66, Is. 1. - Ст. 16218, DOI 10.1103/PhysRevE.66.016218. - Cited References: 36 . - ISSN 1539-3755

РУБ Physics, Fluids & Plasmas + Physics, Mathematical
Рубрики:
PHASE SINGULARITIES
   NODAL POINTS
   WAVE-FIELDS
   QUANTUM
   STREAMLINES
   CONDUCTANCE
   VORTICES
   CHAOS
Кл.слова (ненормированные):
Eigenvalues and eigenfunctions -- Mathematical models -- Networks (circuits) -- Random processes -- Resonance -- Signal processing -- Spurious signal noise -- Bursting time series -- Coherence resonance -- Power spectrum -- Stochastic resonance -- Chaos theory
Аннотация: We discuss signatures of quantum chaos in terms of distributions of nodal points, saddle points, and streamlines for coherent electron transport through two-dimensional billiards, which are either nominally integrable or chaotic. As typical examples of the two cases we select rectangular and Sinai billiards. We have numerically evaluted distribution functions for nearest distances between nodal points and found that there is a generic form for open chaotic billiards through which a net current is passed. We have also evaluated the distribution functions for nodal points with specific vorticity (winding number) as well as for saddle points. The distributions may be used as signatures of quantum chaos in open systems. All distributions are well reproduced using random complex linear combinations of nearly monochromatic states in nominally closed billiards. In the case of rectangular billiards with simple sharp-cornered leads the distributions have characteristic features related to order among the nodal points. A flaring or rounding of the contact regions may, however, induce a crossover to nodal point distributions and current flow typical for quantum chaos. For an irregular arrangement of nodal points, as for example in the Sinai billiard, the quantum flow lines become very complex and volatile, recalling chaos among classical trajectories. Similarities with percolation are pointed out.

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Держатели документа:
Linkoping Univ, Dept Phys & Measurement Technol, S-58183 Linkoping, Sweden
LV Kirenskii Inst Phys, Krasnoyarsk 660036, Russia
ИФ СО РАН
Dept. of Phys. and Msrmt. Technology, Linkoping University, S-581 83 Linkoping, Sweden
Kirensky Institute of Physics, 660036, Krasnoyarsk, Russian Federation

Доп.точки доступа:
Sadreev, A. F.; Садреев, Алмаз Фаттахович; Starikov, A. A.
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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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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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Raman spectra and elastic properties of KPb2Cl5 crystals / A. N. Vtyurin [et al.] ; ed.: A Kaplyanskii, A Akimov, Akimov, // 11th International Conference on Phonon Scattering in Condensed Matter (PHONONS 2004) (JUL 25-30, 2004, St Petersburg, RUSSIA) : WILEY-V C H VERLAG GMBH, 2004. - P. 3142-3145, DOI 10.1002/pssc.200405401. - Cited References: 10 . - ISBN 3-527-40588-7

РУБ Physics, Condensed Matter
Рубрики:
LATTICE-DYNAMICS
Кл.слова (ненормированные):
Computer simulation -- Crystal structure -- Eigenvalues and eigenfunctions -- Halogen compounds -- Nonlinear optics -- Phonons -- Potassium compounds -- Vectors -- Elastic constants -- Heavy cations -- Ionic electron envelopes -- Ionic interactions -- Raman scattering
Аннотация: Raman scattering spectra and elastic constants of KPb2Cl5 crystals have been studied. The results obtained are interpreted in terms of the ab initio lattice dynamics model taking into account multipole moments of ionic electron envelopes. The experimental results have been found to be in good agreement with numerical simulation; the narrow phonon spectra are shown to be due to a considerable contribution of heavy cations into the eigenvectors of the higher frequency lattice modes.

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Держатели документа:
LV Kirenskii Inst Phys, Krasnoyarsk 660036, Russia
Joint Inst Geol Geophys & Mineral, Novosibirsk 630090, Russia
Krasnoyarsk State Univ, Krasnoyarsk 660036, Russia
ИФ СО РАН
Kirensky Institute of Physics, 660036 Krasnoyarsk, Russian Federation
Jt. Inst. Geol., Geophys./Mineral., 630090 Novosibirsk, Russian Federation
Krasnoyarsk State University, 660036 Krasnoyarsk, Russian Federation

Доп.точки доступа:
Vtyurin, A. N.; Втюрин, Александр Николаевич; Isaenko, L. I.; Krylova, S. N.; Крылова, Светлана Николаевна; Yelisseyev, A.; Shebanin, A. P.; Turchin, P. P.; Zamkova, N. G.; Замкова, Наталья Геннадьевна; Zinenko, V. I.; Зиненко, Виктор Иванович
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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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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.
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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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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10.

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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