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Kolovsky, A. R.
Bose-Hubbard Hamiltonian: Quantum Chaos Approach / A. R. Kolovsky // Worksh. Bose-Einstein condens. and quant. chaos. - 2015

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Доп.точки доступа:
Коловский, Андрей Радиевич; Workshop On Bose-Einstein Condensation and Quantum Chaos(2015 ; 30 Mart-2 Apr. ; Sao Paulo, Brasil)
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Kolovsky, A. R.
Landau-Stark states / A. R. Kolovsky // Quantum chaos: fundamentals and applications. - 2015

Материалы конференции

Доп.точки доступа:
Коловский, Андрей Радиевич; "Quantum chaos: fundamentals and applications", Session Workshop (1 (W1) ; 2015 ; Mart ; 14-21 ; Toulose, France)
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    Kolovsky, A. R.
    Bose-Hubbard Hamiltonian: Quantum chaos approach / A. R. Kolovsky // Int. J. Mod. Phys. B. - 2016. - Vol. 30, Is. 10. - Ст. 1630009, DOI 10.1142/S0217979216300097. - Cited References:42 . - ISSN 0217-9792. - ISSN 1793-6578
   Перевод заглавия: Гамильтониан Бозе-Хаббарда: подход с точки зрения квантового хаоса

РУБ Physics, Applied + Physics, Condensed Matter + Physics, Mathematical
Рубрики:
Optical lattice
   Dynamics
   Atoms
   States
   Model
Кл.слова (ненормированные):
Cold atoms in optical lattices -- quantum transport -- nonlinear dynamics and chaos
Аннотация: We discuss applications of the theory of quantum chaos to one of the paradigm models of many-body quantum physics - the Bose-Hubbard (BH) model, which describes, in particular, interacting ultracold Bose atoms in an optical lattice. After preliminary, pure quantum analysis of the system we introduce the classical counterpart of the BH model and the governing semiclassical equations of motion. We analyze these equations for the problem of Bloch oscillations (BOs) of cold atoms where a number of experimental results are available. The paper is written for nonexperts and can be viewed as an introduction to the field.

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Доп.точки доступа:
Коловский, Андрей Радиевич
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Maksimov, D. N.
Gaussian random waves in elastic media / D. N. Maksimov, A. F. Sadreev // JETP Letters. - 2007. - Vol. 86, Is. 9. - P. 584-588, DOI 10.1134/S0021364007210060. - Cited References: 22 . - ISSN 0021-3640

РУБ Physics, Multidisciplinary
Рубрики:
STATISTICAL PROPERTIES
SPECTRAL STATISTICS
CHAOS
Аннотация: Similar to the Berry conjecture of quantum chaos, an elastic analogue which incorporates longitudinal and transverse elastic displacements with corresponding wave vectors is considered. The correlation functions are derived for the amplitudes and intensities of elastic displacements. A comparison to the numerics in a quarter-Bunimovich stadium demonstrates excellent agreement.

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Держатели документа:
[Maksimov, D. N.] Russian Acad Sci, Inst Phys, Krasnoyarsk 660036, Russia
[Sadreev, A. F.] Linkoping Univ, Dept Phys & Measurement Technol, S-58183 Linkoping, Sweden
ИФ СО РАН
Institute of Physics, Russian Academy of Sciences, Krasnoyarsk, 660036, Russian Federation
Department of Physics and Measurement Technology, Linkoping University, SE-581 83 Linkoping, Sweden

Доп.точки доступа:
Sadreev, A. F.; Садреев, Алмаз Фаттахович; Максимов, Дмитрий Николаевич
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Kolovsky, A. R.
Semiclassical analysis of the Bogoliubov spectrum in the Bose-Hubbard model / A. R. Kolovsky // Phys. Rev. E. - 2007. - Vol. 76, Is. 2. - Ст. 26207, DOI 10.1103/PhysRevE.76.026207. - Cited References: 19 . - ISSN 1539-3755

РУБ Physics, Fluids & Plasmas + Physics, Mathematical
Рубрики:
SELF-TRAPPING EQUATION
CHAOS
Кл.слова (ненормированные):
Electron energy levels -- Spectrum analysis -- Bogoliubov spectrum -- Bose Hubbard models -- Excitation dynamics -- Finite size effects -- Elementary particles
Аннотация: We analyze the Bogoliubov spectrum of the Bose-Hubbard model with a finite number of sites and Bose particles by using a semiclassical approach. This approach allows us to take into account the finite-size effects responsible for evolution of the Bogoliubov spectrum into an irregular (chaotic) spectrum at higher energies. A manifestation of this transition for the excitation dynamics of the Bose-Hubbard system is discussed as well.

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Держатели документа:
LV Kirenskii Inst Phys, Krasnoyarsk 660036, Russia
ИФ СО РАН
Kirensky Institute of Physics, 660036 Krasnoyarsk, Russian Federation

Доп.точки доступа:
Коловский, Андрей Радиевич
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Kolovsky, A. R.
Semiclassical quantization of the Bogoliubov spectrum / A. R. Kolovsky // Phys. Rev. Lett. - 2007. - Vol. 99, Is. 2. - Ст. 20401, DOI 10.1103/PhysRevLett.99.020401. - Cited References: 14 . - ISSN 0031-9007

РУБ Physics, Multidisciplinary
Рубрики:
SELF-TRAPPING EQUATION
CHAOS
Кл.слова (ненормированные):
Chaotic systems -- High energy physics -- Mathematical models -- Spectrum analysis -- Bogoliubov spectrum -- Semiclassical quantization -- Bose-Einstein condensation
Аннотация: We analyze the Bogoliubov spectrum of the three-site Bose-Hubbard model with a finite number of Bose particles by using a semiclassical approach. The Bogoliubov spectrum is shown to be associated with the low-energy regular component of the classical Hubbard model. We identify the full set of the integrals of motion of this regular component and, quantizing them, obtain the energy levels of the quantum system. The critical values of the energy, above which the regular Bogoliubov spectrum evolves into a chaotic spectrum, is indicated as well.

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Держатели документа:
LV Kirenskii Inst Phys, Krasnoyarsk 660036, Russia
ИФ СО РАН
Kirensky Institute of Physics, 660036 Krasnoyarsk, Russian Federation

Доп.точки доступа:
Коловский, Андрей Радиевич
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Sadreev, A. F.
Signatures of quantum chaos in complex wavefunctions describing open billiards / A. F. Sadreev, K. F. Berggren // J. Phys. A. - 2005. - Vol. 38, Is. 49. - P. 10787-10804, DOI 10.1088/0305-4470/38/49/019. - Cited References: 103 . - ISSN 0305-4470

РУБ Physics, Multidisciplinary + Physics, Mathematical
Рубрики:
TIME-REVERSAL SYMMETRY
   RANDOM-MATRIX
   STATISTICAL-THEORY
   ENERGY-LEVELS
   S-MATRIX
   CHARACTERISTIC VECTORS
   PHASE SINGULARITIES
   INFINITE DIMENSIONS
   BORDERED MATRICES
   NUCLEAR REACTIONS
Аннотация: We discuss signatures of quantum chaos in open chaotic billiards. Solutions for such a system are given by complex scattering wavefunctions psi = u + iv when a steady current flows through the billiard. For slightly opened chaotic billiards the current distributions are simple and universal. It is remarkable that the resonant transmission through integrable billiards also gives the universal current distribution. Cur-rents induced by the Rashba spin-orbit interaction can flow even in closed billiards. Wavefunction and current distributions for a chaotic billiard with weak and strong spin-orbit interactions have been derived and compared with numerics. Similarities with classical waves are considered. In particular we propose that the networks of electric resonance RLC circuits may be used to study wave chaos. However, being different from quantum billiards, there is a resistance from the inductors which gives rise to heat power and decoherence.

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

Доп.точки доступа:
Berggren, K. F.; Садреев, Алмаз Фаттахович
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Symmetry breaking in a driven and strongly damped pendulum / J. . Isohatala [et al.] // Phys. Rev. E. - 2005. - Vol. 71, Is. 6. - Ст. 66206, DOI 10.1103/PhysRevE.71.066206. - Cited References: 37 . - ISSN 1539-3755

РУБ Physics, Fluids & Plasmas + Physics, Mathematical
Рубрики:
DC VOLTAGE GENERATION
   SEMICONDUCTOR SUPERLATTICES
   JOSEPHSON-JUNCTIONS
   BLOCH OSCILLATIONS
   FORCED PENDULUM
   CHAOS
   FREQUENCY
   SYSTEMS
   RECTIFICATION
   STANDARD
Кл.слова (ненормированные):
Periodically driven pendulums -- Symmetry breaking -- Bifurcation (mathematics) -- Damping -- Dynamics -- Nonlinear systems -- Semiconductor superlattices -- Pendulums
Аннотация: We examine the conditions for appearance of a symmetry breaking bifurcation in damped and periodically driven pendulums in the case of strong damping. We show that symmetry breaking, unlike other nonlinear phenomena, can exist at high dissipation. We prove that symmetry breaking phases exist between phases of symmetric normal and symmetric inverted oscillations. We find that symmetry broken solutions occupy a smaller region of the pendulum's parameter space in comparison to the statements made in earlier considerations [McDonald and Plischke, Phys. Rev. B 27, 201 (1983)]. Our research on symmetry breaking in a strongly damped pendulum is relevant to an understanding of the phenomena of dynamic symmetry breaking and rectification in pure ac driven semiconductor superlattices.

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Держатели документа:
Univ Oulu, Dept Phys Sci, FIN-90014 Oulu, Finland
LV Kirenskii Inst Phys, Theory Nonlinear Proc Lab, Krasnoyarsk 660036, Russia
ИФ СО РАН
Department of Physical Sciences, P. O. Box 3000, Oulu FIN-90014, Finland
Theory of Nonlinear Processes Laboratory, Kirensky Institute of Physics, Krasnoyarsk 660036, Russian Federation

Доп.точки доступа:
Isohatala, J.; Alekseev, K. N.; Kurki, L. T.; Pietilainen, P.
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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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Kolovsky, A. R.
Quantum chaos in the Bose-Hubbard model / A. R. Kolovsky, A. . Buchleitner // Europhys. Lett. - 2004. - Vol. 68, Is. 5. - P. 632-638, DOI 10.1209/epl/i2004-10265-7. - Cited References: 22 . - ISSN 0295-5075

РУБ Physics, Multidisciplinary
Рубрики:
EINSTEIN CONDENSATE
   DOUBLE-WELL
   TRANSITION
   SUPERFLUID
   INSULATOR
   ATOMS
Аннотация: We present a numerical study of the spectral properties of the 1D Bose-Hubbard model. Unlike the 1D Hubbard model for fermions, this system is found to be non-integrable, and exhibits Wigner-Dyson spectral statistics under suitable conditions.

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Держатели документа:
Max Planck Inst Phys Komplexer Syst, D-01187 Dresden, Germany
LV Kirenskii Inst Phys, Krasnoyarsk 660036, Russia
ИФ СО РАН
Max-Planck-Inst. F. Physik K., D-01187 Dresden, Germany
Kirensky Institute of Physics, 660036 Krasnoyarsk, Russian Federation

Доп.точки доступа:
Buchleitner, A.; Коловский, Андрей Радиевич
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11.

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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12.

Sadreev, A. F.
Current statistics for wave transmission through an open Sinai billiard: Effects of net currents / A. F. Sadreev, K. F. Berggren // Phys. Rev. E. - 2004. - Vol. 70, Is. 2. - Ст. 26201, DOI 10.1103/PhysRevE.70.026201. - Cited References: 27 . - ISSN 1539-3755

РУБ Physics, Fluids & Plasmas + Physics, Mathematical
Рубрики:
EIGENVECTOR STATISTICS
   OPEN SYSTEMS
   EIGENFUNCTIONS
   CHAOS
   FLUCTUATIONS
   CROSSOVER
   ELECTRONS
   INTENSITY
Кл.слова (ненормированные):
Acoustic wave transmission -- Boundary conditions -- Computer simulation -- Continuum mechanics -- Current density -- Fermi level -- Mathematical transformations -- Microwaves -- Probability density function -- Quantum theory -- Random processes -- Reverberation -- Statistical methods -- Surface waves -- Waveguides -- Microwave cavities -- Poynting vector -- Sinai billiard -- Wave functions -- Cavity resonators
Аннотация: Transport through quantum and microwave cavities is studied by analytic and numerical techniques. In particular, we consider the statistics for a finite net probability current (Poynting vector) flowing through an open ballistic Sinai billiard to which two opposite leads/wave guides are attached. We show that if the net probability current is small, the scattering wave function inside the billiard is well approximated by a Gaussian random complex field. In this case, the current statistics are universal and obey simple analytic forms. For larger net currents, these forms still apply over several orders of magnitudes. However, small characteristic deviations appear in the tail regions. Although the focus is on electron and microwave billiards, the analysis is relevant also to other classical wave cavities as, for example, open planar acoustic reverberation rooms, elastic membranes, and water surface waves in irregularly shaped vessels.

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

Доп.точки доступа:
Berggren, K. F.; Садреев, Алмаз Фаттахович
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13.

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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14.

Kolovsky, A. R.
Floquet-Bloch operator for the Bose-Hubbard model with static field / A. R. Kolovsky, A. . Buchleitner // Phys. Rev. E. - 2003. - Vol. 68, Is. 5. - Ст. 56213, DOI 10.1103/PhysRevE.68.056213. - Cited References: 23 . - ISSN 1539-3755

РУБ Physics, Fluids & Plasmas + Physics, Mathematical
Рубрики:
QUANTUM CHAOS
CONDENSATE
ATOMS
Аннотация: This paper deals with the spectral properties of the one-dimensional Bose-Hubbard Hamiltonian amended by an external static field-a model for cold spinless atoms loaded in a quasi-one-dimensional optical lattice and subject to an additional static (for example, gravitational) force. The analysis is performed in terms of the Floquet-Bloch operator, defined as the evolution operator of the system over one Bloch period. Depending on the particular choice of parameters, the spectrum is found to be either regular or chaotic. Moreover, in the chaotic case, the matrix of the Floquet-Bloch operator is well characterized as a random matrix of the circular orthogonal ensemble.

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Держатели документа:
Max Planck Inst Phys Komplexer Syst, D-01187 Dresden, Germany
LV Kirenskii Inst Phys, Krasnoyarsk 660036, Russia
ИФ СО РАН

Доп.точки доступа:
Buchleitner, A.; Коловский, Андрей Радиевич
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15.

Chaotic waveguide-based resonators for microlasers / J. A. Mendez-Bermudez [et al.] // Phys. Rev. B. - 2003. - Vol. 67, Is. 16. - Ст. 161104, DOI 10.1103/PhysRevB.67.161104. - Cited References: 33 . - ISSN 1098-0121

РУБ Physics, Condensed Matter
Рубрики:
QUANTUM-CLASSICAL CORRESPONDENCE
   MORPHOLOGY-DEPENDENT RESONANCES
   DIRECTIONAL EMISSION
   OPTICAL CAVITIES
   MICRODISK LASERS
   WAVE CHAOS
   DROPLETS
   PRECESSION
   BILLIARDS
   STATES
Аннотация: We propose the construction of highly directional emission microlasers using two-dimensional high-index semiconductor waveguides as open resonators. The prototype waveguide is formed by two collinear leads connected to a cavity of certain shape. The proposed lasing mechanism requires that the shape of the cavity yield mixed chaotic ray dynamics so as to have the approplate (phase space) resonance islands. These islands allow, via Heisenberg's uncertainty principle, the appearance of quasibound states (QBSs) which, in turn, propitiate the lasing mechanism. The energy values of the QBSs are found through the solution of the Helmholtz equation. We use classical ray dynamics to predict the direction and intensity of the lasing produced by such open resonators for typical values of the index of refraction.

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Держатели документа:
Univ Autonoma Puebla, Inst Fis, Puebla 72570, Mexico
Univ Hradec Kralove, Dept Phys, Hradec Kralove, Czech Republic
Acad Sci Czech Republ, Inst Phys, Prague, Czech Republic
LV Kirenskii Inst Phys, Krasnoyarsk 660036, Russia
ИФ СО РАН

Доп.точки доступа:
Mendez-Bermudez, J. A.; Luna-Acosta, G. A.; Seba, P.; Pichugin, K. N.; Пичугин, Константин Николаевич
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16.

Alekseev, K. N.
Pendulum limit, chaos and phase-locking in the dynamics of ac-driven semiconductor superlattices / K. N. Alekseev, F. V. Kusmartsev // Phys. Lett. A. - 2002. - Vol. 305, Is. 5. - P. 281-288, DOI 10.1016/S0375-9601(02)01420-2. - Cited References: 60 . - ISSN 0375-9601

РУБ Physics, Multidisciplinary
Рубрики:
STRANGE NONCHAOTIC ATTRACTORS
   DC VOLTAGE GENERATION
   JOSEPHSON-JUNCTIONS
   GAAS/ALAS SUPERLATTICE
   BLOCH OSCILLATIONS
   TERAHERTZ RADIATION
   ELECTRIC-FIELD
   THZ RADIATION
   FREQUENCY
   TRANSPORT
Кл.слова (ненормированные):
semiconductor superlattice -- pendulum -- chaos -- phase-locking -- Josephson junction -- Chaos -- Josephson junction -- Pendulum -- Phase-locking -- Semiconductor superlattice -- analytic method -- analytical parameters -- article -- dynamics -- electric potential -- semiconductor -- temperature
Аннотация: We describe a limiting case when nonlinear dynamics of an ac-driven semiconductor superlattice in the miniband transport regime is governed by a periodically forced and damped pendulum equations. We find analytically the conditions for a transition to chaos. With increasing temperature the chaos disappears. We also discuss fractional do voltage states in a superlattice originating from phase-locked states of the pendulum. (C) 2002 Elsevier Science B.V. All rights reserved.

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Держатели документа:
Oulu Univ, Dept Phys Sci, FIN-90014 Oulu, Finland
LV Kirenskii Inst Phys, Theory Nonlinear Proc Lab, Krasnoyarsk 660036, Russia
Loughborough Univ Technol, Dept Phys, Loughborough LE11 3TU, Leics, England
ИФ СО РАН
Department of Physical Sciences, University of Oulu, P.O. Box 3000, FIN-90014, Oulu, Finland
Theory of Nonlin. Proc. Laboratory, Kirensky Institute of Physics, Krasnoyarsk 660036, Russian Federation
Department of Physics, Loughborough University, Loughborough LE11 3TU, United Kingdom

Доп.точки доступа:
Kusmartsev, F. V.
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17.

Understanding quantum scattering properties in terms of purely classical dynamics: Two-dimensional open chaotic billiards / J. A. Mendez-Bermudez [et al.] // Phys. Rev. E. - 2002. - Vol. 66, Is. 4. - Ст. 46207, DOI 10.1103/PhysRevE.66.046207. - Cited References: 34 . - ISSN 1539-3755

РУБ Physics, Fluids & Plasmas + Physics, Mathematical
Рубрики:
BALLISTIC-TRANSPORT
   POINCARE SECTIONS
   CAVITIES
   EIGENFUNCTIONS
   LOCALIZATION
   CHANNEL
Кл.слова (ненормированные):
Chaos theory -- Electron tunneling -- Laser applications -- Nonlinear systems -- Probability -- Waveguide components -- Chaotic motion -- Microlasers -- Quantum scattering -- Scattering probability -- Quantum theory -- article
Аннотация: We study classical and quantum scattering properties of particles in the ballistic regime in two-dimensional chaotic billiards that are models of electron- or micro-waveguides. To this end we construct the purely classical counterparts of the scattering probability (SP) matrix \S(n,m)\(2) and Husimi distributions specializing to the case of mixed chaotic motion (incomplete horseshoe). Comparison between classical and quantum quantities allows us to discover the purely classical dynamical origin of certain general as well as particular features that appear in the quantum description of the system. On the other hand, at certain values of energy the tunneling of the wave function into classically forbidden regions produces striking differences between the classical and quantum quantities. A potential application of this phenomenon in the field of microlasers is discussed briefly. We also see the manifestation of whispering gallery orbits as a self-similar structure in the transmission part of the classical SP matrix.

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Держатели документа:
Univ Autonoma Puebla, Inst Fis, Puebla 72570, Mexico
Univ Hradec Kralove, Dept Phys, Hradec Kralove, Czech Republic
Acad Sci Czech Republ, Inst Phys, Prague, Czech Republic
LV Kirenskii Inst Phys, Krasnoyarsk 660036, Russia
ИФ СО РАН
Instituto de Fisica, Univ. Autonoma de Puebla, Apartado Postal J-48, Puebla 72570, Mexico
Department of Physics, University Hradec Kralove, Hradec Kralove, Czech Republic
Institute of Physics, Czech Academy of Sciences, Cukrovarnicka 10, Prague, Czech Republic
Kirensky Institute of Physics, 660036 Krasnoyarsk, Russian Federation

Доп.точки доступа:
Mendez-Bermudez, J. A.; Luna-Acosta, G. A.; Seba, P.; Pichugin, K. N.; Пичугин, Константин Николаевич
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18.

Gluck, M.
Wannier-Stark resonances in optical and semiconductor superlattices / M. . Gluck, A. R. Kolovsky, H. J. Korsch // Phys. Rep.-Rev. Sec. Phys. Lett. - 2002. - Vol. 366, Is. 3. - P. 103-182, DOI 10.1016/S0370-1573(02)00142-4. - Cited References: 234 . - ISSN 0370-1573

РУБ Physics, Multidisciplinary
Рубрики:
UNIFORM ELECTRIC-FIELD
   QUANTUM CHAOTIC SCATTERING
   FRANZ-KELDYSH OSCILLATIONS
   METAL-INSULATOR-TRANSITION
   ALTERNATING SITE ENERGIES
   GAAS-ALAS SUPERLATTICES
   RANDOM UNITARY MATRICES
   WAVE-GUIDE ARRAYS
   BLOCH OSCILLATIONS
   PERTURBATION-THEORY
Кл.слова (ненормированные):
Wannier-Stark resonances -- semiconductor superlattices -- optical lattices -- resonance statistics -- quantum chaos -- Optical lattices -- Quantum chaos -- Resonances statistics -- Semiconductor superlattices -- Wannier-Stark resonances
Аннотация: In this work, we discuss the resonance states of a quantum particle in a periodic potential plus a static force. Originally, this problem was formulated for a crystal electron subject to a static electric field and it is nowadays known as the Wannier-Stark problem. We describe a novel approach to the Wannier-Stark problem developed in recent years. This approach allows to compute the complex energy spectrum of a Wannier-Stark system as the poles of a rigorously constructed scattering matrix and solves the Wannier-Stark problem without any approximation. The suggested method is very efficient from the numerical point of view and has proven to be a powerful analytic tool for Wannier-Stark resonances appearing in different physical systems such as optical lattices or semiconductor superlattices. (C) 2002 Elsevier Science B.V. All rights reserved.

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Держатели документа:
Univ Kaiserslautern, Fachbereich Phys, D-67653 Kaiserslautern, Germany
LV Kirenskii Inst Phys, Krasnoyarsk 660036, Russia
ИФ СО РАН
Fachbereich (FB) Physik, Universitat Kaiserslautern, D-67653 Kaiserslautern, Germany
L.V. Kirensky Institute of Physics, 660036 Krasnoyarsk, Russian Federation

Доп.точки доступа:
Kolovsky, A. R.; Коловский, Андрей Радиевич; Korsch, H. J.
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19.

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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20.

Classical versus quantum structure of the scattering probability matrix: Chaotic waveguides / G. A. Luna-Acosta [et al.] // Phys. Rev. E. - 2002. - Vol. 65, Is. 4. - Ст. 46605, DOI 10.1103/PhysRevE.65.046605. - Cited References: 47 . - ISSN 1539-3755

РУБ Physics, Fluids & Plasmas + Physics, Mathematical
Рубрики:
SEMICLASSICAL CROSS-SECTION
   CONDUCTANCE FLUCTUATIONS
   S-MATRIX
   BALLISTIC-TRANSPORT
   WEAK-LOCALIZATION
   CAVITIES
   COLLISIONS
   MICROSTRUCTURES
   DENSITY
   CHANNEL
Кл.слова (ненормированные):
Chaos theory -- Matrix algebra -- Optical waveguides -- Quantum theory -- Scattering -- Wave equations -- Chaotic cavities -- Chaotic waveguides -- Quantum structure -- Scattering probability matrix -- Quantum optics
Аннотация: The purely classical counterpart of the scattering probability matrix (SPM) \S(n,m)\(2) of the quantum scattering matrix S is defined for two-dimensional quantum waveguides for an arbitrary number of propagating modes M. We compare the quantum and classical structures of \S(n,m)\(2) for a waveguide with generic Hamiltonian chaos. It is shown that even for a moderate number of channels, knowledge of the classical structure of the SPM allows us to predict the global structure of the quantum one and, hence, understand important quantum transport properties of waveguides in terms of purely classical dynamics. It is also shown that the SPM, being an intensity measure, can give additional dynamical information to that obtained by the Poincare maps.

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Держатели документа:
Univ Autonoma Puebla, Inst Fis, Puebla 72570, Mexico
Univ Hradec Kralove, Dept Phys, Hradec Kralove, Czech Republic
Acad Sci Czech Republ, Inst Phys, Prague, Czech Republic
LV Kirenskii Inst Phys, Krasnoyarsk 660036, Russia
ИФ СО РАН
Instituto de Fisica, Univ. Autonoma de Puebla, Apartado Postal J-48, Puebla 72570, Mexico
Department of Physics, University Haradec Kralove, Hradec Kralove, Czech Republic
Institute of Physics, Czech Academy of Sciences, Cukrovarnicka 10, Prague, Czech Republic
Kirensky Institute of Physics, 660036 Krasnoyarsk, Russian Federation

Доп.точки доступа:
Luna-Acosta, G. A.; Mendez-Bermudez, J. A.; Seba, P.; Pichugin, K. N.; Пичугин, Константин Николаевич
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