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Вид документа : Статья из журнала
Шифр издания :
Автор(ы) : Tanner G., Chappell D. J., Maksimov D. N.
Заглавие : Wave Intensity Distributions in Complex Structures
Коллективы : Workshop on Quantum Chaos and Localisation Phenomena
Место публикации : Acta Phys. Pol. A. - 2011. - Vol. 120, Is. 6A. - P.A172-A177. - ISSN 0587-4246
Примечания : Cited References: 19
Предметные рубрики: STATISTICAL ENERGY ANALYSIS
HIGH-FREQUENCIES
SYSTEMS
VIBRATIONS
Аннотация: The vibro-acoustic response of mechanical structures can in general be well approximated in terms of linear wave equations. Standard numerical solution methods comprise the finite or boundary element method in the low frequency regime and statistical energy analysis in the high-frequency limit. Major computational challenges are posed by the so-called mid-frequency problem - that is, composite structures where the local wavelength may vary by orders of magnitude across the components. Recently, a new approach towards determining the distribution of mechanical and acoustic wave energy in complex built-up structures improving on standard statistical energy analysis has been proposed. The technique interpolates between statistical energy analysis and ray tracing containing both these methods as limiting cases. The method has its origin in studying solutions of wave equation with an underlying chaotic ray-dynamics - often referred to as wave chaos. Within the new theory dynamical energy analysis - statistical energy analysis is identified as a low resolution ray tracing algorithm and typical statistical energy analysis assumptions can be quantified in terms of the properties of the ray dynamics. We have furthermore developed a hybrid statistical energy analysis/finite element method based on random wave model assumptions for the short-wavelength components. This makes it possible to tackle mid-frequency problems under certain constraints on the geometry of the structure. Dynamical energy analysis and statistical energy analysis/finite element method calculations for a range of multi-component model systems will be presented. The results are compared with both statistical energy analysis results and finite element method as well as boundary element method calculations. Dynamical energy analysis emerges as a numerically efficient method for calculating mean wave intensities with a high degree of spatial resolution and capturing long range correlations in the ray dynamics.
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Вид документа : Статья из журнала
Шифр издания :
Автор(ы) : Gluck M., Kolovsky A. R., Korsch H. J.
Заглавие : Wannier-Stark resonances in optical and semiconductor superlattices
Место публикации : Phys. Rep.-Rev. Sec. Phys. Lett.: ELSEVIER SCIENCE BV, 2002. - Vol. 366, Is. 3. - P103-182. - ISSN 0370-1573, DOI 10.1016/S0370-1573(02)00142-4
Примечания : Cited References: 234
Предметные 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
Ключевые слова (''Своб.индексиров.''): 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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Вид документа : Статья из журнала
Шифр издания :
Автор(ы) : Mendez-Bermudez J. A., Luna-Acosta G. A., Seba P., Pichugin K. N.
Заглавие : Understanding quantum scattering properties in terms of purely classical dynamics: Two-dimensional open chaotic billiards
Место публикации : Phys. Rev. E: AMER PHYSICAL SOC, 2002. - Vol. 66, Is. 4. - Ст.46207. - ISSN 1539-3755, DOI 10.1103/PhysRevE.66.046207
Примечания : Cited References: 34
Предметные рубрики: BALLISTIC-TRANSPORT
POINCARE SECTIONS
CAVITIES
EIGENFUNCTIONS
LOCALIZATION
CHANNEL
Ключевые слова (''Своб.индексиров.''): 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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Вид документа : Статья из журнала
Шифр издания :
Автор(ы) : Alekseev K. N., Perina J.
Заглавие : The 1/N-expansion, quantum-classical correspondence and nonclassical states generation in dissipative higher-order anharmonic oscillators
Место публикации : Phys. Scr.: ROYAL SWEDISH ACAD SCIENCES, 2000. - Vol. 61, Is. 1. - P7-16. - ISSN 0281-1847, DOI 10.1238/Physica.Regular.061a00007
Примечания : Cited References: 38
Предметные рубрики: 2ND-HARMONIC GENERATION
HARMONIC-GENERATION
SQUEEZED STATES
CHAOS
LIGHT
MECHANICS
DYNAMICS
STATISTICS
SYSTEMS
OPTICS
Аннотация: We develop a method for the determination of the dynamics of dissipative quantum systems in the limit of large number of quanta N, based on the 1/N-expansion of Heidmann et al. [Opt. Commun. 54, 189 (1985)] and the quantum-classical correspondence. Using this method, we End analytically the dynamics of nonclassical states generation in the higher-order anharmonic dissipative oscillators for an arbitrary temperature of a reservoir. We show that the quantum correction to the classical motion increases with time quadratically up to some maximal value, which is dependent on the degree of nonlinearity and a damping constant, and then it decreases. Similarities and differences with the corresponding behavior of the quantum corrections to the classical motion in the Hamiltonian chaotic systems are discussed. We also compare our results obtained for some limiting cases with the results obtained by using other semiclassical tools and discuss the conditions for validity of our approach.
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Вид документа : Статья из журнала
Шифр издания :
Автор(ы) : Isohatala J., Alekseev K. N., Kurki L. T., Pietilainen P.
Заглавие : Symmetry breaking in a driven and strongly damped pendulum
Место публикации : Phys. Rev. E: AMERICAN PHYSICAL SOC, 2005. - Vol. 71, Is. 6. - Ст.66206. - ISSN 1539-3755, DOI 10.1103/PhysRevE.71.066206
Примечания : Cited References: 37
Предметные рубрики: DC VOLTAGE GENERATION
SEMICONDUCTOR SUPERLATTICES
JOSEPHSON-JUNCTIONS
BLOCH OSCILLATIONS
FORCED PENDULUM
CHAOS
FREQUENCY
SYSTEMS
RECTIFICATION
STANDARD
Ключевые слова (''Своб.индексиров.''): 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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Вид документа : Статья из журнала
Шифр издания :
Автор(ы) : Berman G. P., Iomin A. M.
Заглавие : Structural order ND chaos in a one-dimensional quantum atomic chain
Место публикации : Phys. Lett. A. - 1985. - Vol. 107, Is. 7. - P.324-328. - ISSN 0375-9601, DOI 10.1016/0375-9601(85)90646-2
Примечания : Cited References: 22
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Вид документа : Статья из сборника (однотомник)
Шифр издания :
Автор(ы) : Korets A.Ya., Krylov A.S., Mironov E.V.
Заглавие : Structural heterogeneity detonation diamond-containing mate rial
Коллективы : Chaotic modeling and Simulation International Conference
Место публикации : 3rd Chaotic modeling and Simulation International Conference: CHAOS 2010. - 2010. - С. 34
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Вид документа : Статья из журнала
Шифр издания :
Автор(ы) : Bulgakov E. N., Sadreev A. F.
Заглавие : Statistics of wave functions and currents induced by spin-orbit interaction in chaotic billiards
Место публикации : Phys. Rev. E: AMER PHYSICAL SOC, 2004. - Vol. 70, Is. 5. - Ст.56211. - ISSN 1539-3755, DOI 10.1103/PhysRevE.70.056211
Примечания : Cited References: 33
Предметные рубрики: HELMHOLTZ-EQUATION
PERSISTENT CURRENTS
ELECTRON-GAS
RINGS
EIGENFUNCTIONS
SYSTEMS
PHASE
Ключевые слова (''Своб.индексиров.''): 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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Вид документа : Статья из журнала
Шифр издания :
Автор(ы) : Kolovsky A. R.
Заглавие : Stationary response of a multilevel quantum system in the regime of quantum chaos
Место публикации : Phys. Lett. A. - 1990. - Vol. 148, Is. 1-2. - P.72-77. - ISSN 0375-9601, DOI 10.1016/0375-9601(90)90579-D
Примечания : Cited References: 19
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10.

Вид документа : Статья из журнала
Шифр издания :
Автор(ы) : Drokin N. A., Ganiev S. M.
Заглавие : Static and dynamic characteristics of the bulk and contact electric resistivity in CDCR2SE4 under stochastic current instability
Место публикации : Fiz. Tverd. Tela. - 1992. - Vol. 34, Is. 7. - P.2122-2128. - ISSN 0367-3294
Примечания : Cited References: 21
Предметные рубрики: OSCILLATIONS
CHAOS
GE
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11.

Вид документа : Статья из журнала
Шифр издания :
Автор(ы) : Alekseev K. N., Priimak D. S.
Заглавие : Squeezed states and quantum chaos
Место публикации : J. Exp. Theor. Phys.: AMER INST PHYSICS, 1998. - Vol. 86, Is. 1. - P61-70. - ISSN 1063-7761, DOI 10.1134/1.558469
Примечания : Cited References: 41
Предметные рубрики: PERIODICALLY KICKED PENDULUM
CLASSICAL CORRESPONDENCE
SYSTEMS
LIGHT
FLUCTUATIONS
OSCILLATOR
MECHANICS
MASER
Аннотация: We examine the dynamics of a wave packet that initially corresponds to a coherent state in the model of a quantum rotator excited by a periodic sequence of kicks. This model is the main model of quantum chaos and allows for a transition from regular behavior to chaotic in the classical limit. By doing a numerical experiment we study the generation of squeezed states in quasiclassical conditions and in a time interval when quantum-classical correspondence is well-defined. We find that the degree of squeezing depends on the degree of local instability in the system and increases with the Chirikov classical stochasticity parameter. We also discuss the dependence of the degree of squeezing on the initial width of the packet, the problem of stability and observability of squeezed states in the transition to quantum chaos, and the dynamics of disintegration of wave packets in quantum chaos. (C) 1998 American Institute of Physics.
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12.

Вид документа : Статья из журнала
Шифр издания :
Автор(ы) : Alekseev K. N., Cannon E. H., McKinney J. C., Kusmartsev F. V., Campbell D. K.
Заглавие : Spontaneous dc current generation in a resistively shunted semiconductor superlattice driven by a terahertz field
Место публикации : Phys. Rev. Lett.: AMERICAN PHYSICAL SOC, 1998. - Vol. 80, Is. 12. - P2669-2672. - ISSN 0031-9007, DOI 10.1103/PhysRevLett.80.2669
Примечания : Cited References: 21
Предметные рубрики: DYNAMIC LOCALIZATION
BLOCH OSCILLATIONS
ELECTRIC-FIELD
THZ-FIELD
PENDULUM
CHAOS
TIME
SUPPRESSION
SYSTEMS
Аннотация: We study a resistively shunted semiconductor superlattice subject to a high-frequency electric field. Using a balance equation approach that incorporates the influence of the electric circuit, we determine numerically a range of amplitude and frequency of the ac field for which a de bias and current are generated spontaneously and show that this region is likely accessible to current experiments. Our simulations reveal that the Bloch frequency corresponding to the spontaneous de bias is approximately an integer multiple of the ac field frequency.
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13.

Вид документа : Статья из журнала
Шифр издания :
Автор(ы) : Berggren K. F., Pichugin K. N., Sadreev A. F., Starikov A. A.
Заглавие : Signatures of quantum chaos in the nodal points and streamlines in electron transport through billiards
Разночтения заглавия :us: Signature of quantum chaos in the nodal points and streamlines in electron transport through billiards
Место публикации : JETP Letters. - 1999. - Vol. 70, Is. 6. - P.403-409. - ISSN 0021-3640, DOI 10.1134/1.568188
Примечания : Cited References: 13
Предметные рубрики:
Аннотация: Streamlines and the distributions of nodal points are used as signatures of chaos in coherent electron transport through three types of billiards: Sinai, Bunimovich, and rectangular. Numerical averaged distribution functions of the nearest distances between nodal points are presented. We find the same form for the Sinai and Bunimovich billiards and suggest that there is a universal form that can be used as a signature of quantum chaos for electron transport in open billiards. The universal distribution function is found to be insensitive to the way the averaging is performed (over the positions of the leads, over an energy interval with a few conductance fluctuations, or both). The integrable rectangular billiard, on the other hand, displays a nonuniversal distribution with a central peak related to partial order of nodal points for the case of symmetric attachment of the leads. However, cases with asymmetric leads tend to the universal form. Also, it is shown how nodal points in the rectangular billiard can lead to "channeling of quantum flows," while disorder in the nodal points in the Sinai billiard gives rise to unstable irregular behavior of the flow. (C) 1999 American Institute of Physics. [S0021- 3640(99)00718-5].
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14.

Вид документа : Статья из журнала
Шифр издания :
Автор(ы) : Sadreev A. F., Berggren K. F.
Заглавие : Signatures of quantum chaos in complex wavefunctions describing open billiards
Место публикации : J. Phys. A. - 2005. - Vol. 38, Is. 49. - P.10787-10804. - ISSN 0305-4470, DOI 10.1088/0305-4470/38/49/019
Примечания : Cited References: 103
Предметные 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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15.

Вид документа : Статья из журнала
Шифр издания :
Автор(ы) : Muraev P. S., Maksimov D. N., Kolovsky A. R.
Заглавие : Signatures of quantum chaos and fermionization in the incoherent transport of bosonic carriers in the Bose-Hubbard chain
Колич.характеристики :5 с
Место публикации : Phys. Rev. E. - 2024. - Vol. 109, Is. 3. - Ст.L032107. - ISSN 24700045 (ISSN), DOI 10.1103/PhysRevE.109.L032107. - ISSN 24700053 (eISSN)
Примечания : Cited References: 34. - The authors acknowledge financial support from the Ministry of Science and Higher Education of Russian Federation (Project No. FSRZ-2023-0006)
Аннотация: We analyze the stationary current of Bose particles across the Bose-Hubbard chain connected to a battery, focusing on the effect of interparticle interactions. It is shown that the current magnitude drastically decreases as the strength of interparticle interactions exceeds the critical value which marks the transition to quantum chaos in the Bose-Hubbard Hamiltonian. We found that this transition is well reflected in the nonequilibrium many-body density matrix of the system. Namely, the level-spacing distribution for eigenvalues of the density matrix changes from Poisson to Wigner-Dyson distributions. With the further increase of the interaction strength, the Wigner-Dyson spectrum statistics change back to the Poisson statistics which now marks fermionization of the Bose particles. With respect to the stationary current, this leads to the counter-intuitive dependence of the current magnitude on the particle number.
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16.

Вид документа : Статья из журнала
Шифр издания :
Автор(ы) : Kolovsky A. R.
Заглавие : Semiclassical quantization of the Bogoliubov spectrum
Разночтения заглавия :авие SCOPUS: Semiclassical quantization of the bogoliubov spectrum
Место публикации : Phys. Rev. Lett.: AMER PHYSICAL SOC, 2007. - Vol. 99, Is. 2. - Ст.20401. - ISSN 0031-9007, DOI 10.1103/PhysRevLett.99.020401
Примечания : Cited References: 14
Предметные рубрики: SELF-TRAPPING EQUATION
CHAOS
Ключевые слова (''Своб.индексиров.''): 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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17.

Вид документа : Статья из журнала
Шифр издания :
Автор(ы) : Kolovsky A. R.
Заглавие : Semiclassical analysis of the Bogoliubov spectrum in the Bose-Hubbard model
Место публикации : Phys. Rev. E: AMER PHYSICAL SOC, 2007. - Vol. 76, Is. 2. - Ст.26207. - ISSN 1539-3755, DOI 10.1103/PhysRevE.76.026207
Примечания : Cited References: 19
Предметные рубрики: SELF-TRAPPING EQUATION
CHAOS
Ключевые слова (''Своб.индексиров.''): 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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18.

Вид документа : Статья из журнала
Шифр издания :
Автор(ы) : Kolovsky A. R.
Заглавие : Relativistic chaos for an electron in a standing microwave field
Место публикации : Europhys. Lett. - 1998. - Vol. 41, Is. 3. - P.257-260. - ISSN 0295-5075, DOI 10.1209/epl/i1998-00139-0
Примечания : Cited References: 9
Предметные рубрики: BEAM
Аннотация: We study the dynamics of an electron in a standing wave of a microwave field. For large field amplitude the system undergoes a transition to a chaotic regime which is shown to be entirely related with the transition to relativistic dynamics. A possible laboratory experiment is shortly discussed.
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19.

Вид документа : Статья из журнала
Шифр издания :
Автор(ы) : Bulgakov E. N., Sadreev A. F.
Заглавие : Rectangular microwave resonators with magnetic anisotropy. Mapping onto pseudointegrable rhombus
Место публикации : Europhys. Lett. - 2002. - Vol. 57, Is. 2. - P.198-204. - ISSN 0295-5075, DOI 10.1209/epl/i2002-00561-8
Примечания : Cited References: 24
Предметные рубрики: TIME-REVERSAL SYMMETRY
SPECTRAL STATISTICS
STADIUM BILLIARD
EIGENFUNCTIONS
SYSTEMS
CHAOS
Аннотация: A rectangular microwave resonator filled with ferrite with uniaxial magnetic anisotropy is considered. It is shown that this task can be reduced to an empty rhombus resonator with the vertex angle defined by an external magnetic field, provided that the magnetic anisotropy of the ferrite is strong. Therefore, the statistics of eigenfrequencies for TM modes is described by the Brody or semi-Poisson distribution with some exceptional cases.
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20.

Вид документа : Статья из журнала
Шифр издания :
Автор(ы) : Alekseev K. N., Alekseeva N. V., Perina J.
Заглавие : Quantum-classical correspondence and nonclassical state generation in dissipative quantum optical systems
Место публикации : J. Exp. Theor. Phys.: AMER INST PHYSICS, 2000. - Vol. 90, Is. 4. - P592-599. - ISSN 1063-7761, DOI 10.1134/1.559142
Примечания : Cited References: 32
Предметные рубрики: 2ND-HARMONIC GENERATION
STATISTICAL PROPERTIES
HARMONIC-GENERATION
SQUEEZED STATES
CHAOS
LIGHT
NONLINEARITIES
INSTABILITIES
DYNAMICS
ATOMS
Аннотация: We develop a semiclassical method to determine the nonlinear dynamics of dissipative quantum optical systems in the limit of large number of photons N; it is based on the 1/N-expansion and the quantum-classical correspondence. The method is used to tackle two problems: the study of the dynamics of nonclassical state generation in higher order anharmonic dissipative oscillators and the establishment of the difference between the quantum and classical dynamics of the second-harmonic generation in a self-pulsing regime. In addressing the first problem, we obtain an explicit time dependence of the squeezing and the Fano factor for an arbitrary degree of anharmonism in the short-time approximation. For the second problem, we analytically find a characteristic time scale at which the quantum dynamics differs insignificantly from the classical one. (C) 2000 MAIK "Nauka/Interperiodica".
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