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Berman, G. P.
Structural order ND chaos in a one-dimensional quantum atomic chain / G. P. Berman, A. M. Iomin // Phys. Lett. A. - 1985. - Vol. 107, Is. 7. - P. 324-328, DOI 10.1016/0375-9601(85)90646-2. - Cited References: 22 . - ISSN 0375-9601

РУБ Physics, Multidisciplinary

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Доп.точки доступа:
Iomin, A. M.; Берман, Геннадий Петрович
}
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Belobrov, P. I.
Methods of nonlinear dynamics and equilibrium structures of magnetoelastic chains / P. I. Belobrov, A. G. Tretyakov, G. M. Zaslavsky // J. Stat. Phys. - 1985. - Vol. 38, Is. 1-2. - P. 393-404, DOI 10.1007/BF01017869. - Cited References: 22 . - ISSN 0022-4715

РУБ Physics, Mathematical

Кл.слова (ненормированные):
chaos -- Incommensurate structure -- magnetoelastic interaction -- nonlinear resonance

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Scopus
Держатели документа:
L. V. Kirensky Institute of Physics, USSR Academy of Sciences Siberian Branch, Krasnoyarsk, 660036, Russia

Доп.точки доступа:
Tretyakov, A. G.; Третьяков, Александр Григорьевич; Zaslavsky, G. M.; Заславский, Георгий Моисеевич; Белобров, Петр Иванович
}
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Kolovsky, A. R.
Stationary response of a multilevel quantum system in the regime of quantum chaos / A. R. Kolovsky // Phys. Lett. A. - 1990. - Vol. 148, Is. 1-2. - P. 72-77, DOI 10.1016/0375-9601(90)90579-D. - Cited References: 19 . - ISSN 0375-9601

РУБ Physics, Multidisciplinary

WOS
Доп.точки доступа:
Коловский, Андрей Радиевич
}
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Dissipative chaos in semiconductor superlattices / K. N. Alekseev [et al.] // Phys. Rev. B. - 1996. - Vol. 54, Is. 15. - P. 10625-10636, DOI 10.1103/PhysRevB.54.10625. - Cited References: 89 . - ISSN 0163-1829

РУБ Physics, Condensed Matter
Рубрики:
NEGATIVE DIFFERENTIAL CONDUCTIVITY
   INJECTED SIGNAL
   BLOCH OSCILLATIONS
   COLLECTIVE EXCITATIONS
   DETERMINISTIC CHAOS
   MINIBAND TRANSPORT
   SURFACE-PLASMONS
   TIME-SERIES
   LASER
   VELOCITY
Аннотация: We consider the motion of ballistic electrons in a miniband of a semiconductor superlattice (SSL) under the influence of an external, time-periodic electric field. We use a semiclassical, balance-equation approach, which incorporates elastic and inelastic scattering (as dissipation) and the self-consistent field generated by the electron motion. The coupling of electrons in the miniband to the self-consistent held produces a cooperative nonlinear oscillatory mode which, when interacting with the oscillatory external field and the intrinsic Bloch-type oscillatory mode, can lead to complicated dynamics, including dissipative chaos. For a range of values of the dissipation parameters we determine the regions in the amplitude-frequency plane of the external field in which chaos can occur. Our results suggest that for terahertz external fields of the amplitudes achieved by present-day free-electron lasers, chaos may be observable in SSL's. We clarify the nature of this interesting nonlinear dynamics in the superlattice-external-field system by exploring analogies to the Dicke model of an ensemble of two-level atoms coupled with a resonant cavity field, and to Josephson junctions.

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Держатели документа:
LOS ALAMOS NATL LAB,DIV THEORET,LOS ALAMOS,NM 87545
LV KIRENSKII INST PHYS,KRASNOYARSK 660036,RUSSIA
UNIV ILLINOIS,DEPT PHYS,URBANA,IL 61801
ИФ СО РАН

Доп.точки доступа:
Alekseev, K. N.; Berman, G. P.; Campbell, D. K.; Cannon, E. H.; Cargo, M. C.
}
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Beloshapkin, V. V.
On the spectral properties of dynamical-systems in the transition region from order to chaos / V. V. Beloshapkin, G. M. Zaslavskii // Phys. Lett. A. - 1983. - Vol. 97, Is. 4. - P. 121-124, DOI 10.1016/0375-9601(83)90191-3. - Cited References: 13 . - ISSN 0375-9601

РУБ Physics, Multidisciplinary

WOS
Доп.точки доступа:
Zaslavsky, G. M.; Заславский, Георгий Моисеевич; Белошапкин, Валерий Васильевич
}
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Vlasova, O. F.
Dissipation effect on chaos onset in a 2-resonance overlap case / O. F. Vlasova, G. M. Zaslavsky // Phys. Lett. A. - 1983. - Vol. 99, Is. 9. - P. 405-410, DOI 10.1016/0375-9601(83)90943-X. - Cited References: 9 . - ISSN 0375-9601

РУБ Physics, Multidisciplinary

WOS
Доп.точки доступа:
Zaslavsky, G. M.; Заславский, Георгий Моисеевич
}
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DYNAMICAL CHAOS IN SU(2) CIRCLE-TIMES-U (1) THEORY / G. . BERMAN [et al.] // Phys. Lett. A. - 1994. - Vol. 194, Is. 4. - P. 251-264, DOI 10.1016/0375-9601(94)91247-5. - Cited References: 26 . - ISSN 0375-9601

РУБ Physics, Multidisciplinary
Рубрики:
GAUGE-THEORY
SYSTEMS
FIELDS
Аннотация: We study the dynamics of the classical homogeneous SU(2) x U(1) gauge theory in the spontaneously broken phase. A transition from regular to chaotic dynamics is shown to occur for energy densities epsilon 0.3m(w)2/G(F) almost-equal-to 2 x 10(10) GeV/fm3. The regular regime is characterized by a sharp frequency spectrum for the Yang-Mills fields. The frequency spectrum in the chaotic regime is continuous and the sharp frequency lines of the regular regime are dispersed. In the early universe or at high energy densities in a Yang-Mills plasma this transition may have observable effects that can be studied by analyzing the frequency spectrum and the time correlation functions. In the chaotic regime these time correlation functions decay considerably faster than in the regular regime.

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Держатели документа:
KIRENSKY PHYS INST,KRASNOYARSK 660036,RUSSIA
LOS ALAMOS NATL LAB,DIV THEORET,LOS ALAMOS,NM 87545
ИФ СО РАН

Доп.точки доступа:
BERMAN, G.; Bulgakov, E. N.; Булгаков, Евгений Николаевич; HOLM, D.; KLUGER, Y.
}
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Spontaneous dc current generation in a resistively shunted semiconductor superlattice driven by a terahertz field / K. N. Alekseev [et al.] // Phys. Rev. Lett. - 1998. - Vol. 80, Is. 12. - P. 2669-2672, DOI 10.1103/PhysRevLett.80.2669. - Cited References: 21 . - ISSN 0031-9007

РУБ Physics, Multidisciplinary
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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Держатели документа:
Univ Illinois, Dept Phys, Urbana, IL 61801 USA
NORDITA, DK-2100 Copenhagen O, Denmark
LV Kirensky Phys Inst, Theory Nonlinear Proc Lab, Krasnoyarsk 660036, Russia
Loughborough Univ Technol, Dept Phys, Loughborough LE11 3TU, Leics, England
ИФ СО РАН

Доп.точки доступа:
Alekseev, K. N.; Cannon, E. H.; McKinney, J. C.; Kusmartsev, F. V.; Campbell, D. K.
}
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Alekseev, K. N.
Light squeezing at the transition to quantum chaos / K. N. Alekseev, J. . Perina // Phys. Rev. E. - 1998. - Vol. 57, Is. 4. - P. 4023-4034, DOI 10.1103/PhysRevE.57.4023. - Cited References: 62 . - ISSN 1063-651X

РУБ Physics, Fluids & Plasmas + Physics, Mathematical
Рубрики:
HIGHLY-EXCITED ATOMS
   ELECTROMAGNETIC-FIELD
   ANHARMONIC-OSCILLATOR
   MICROWAVE IONIZATION
   MONOCHROMATIC-FIELD
   CLASSICAL MECHANICS
   PERIODIC-ORBITS
   RYDBERG ATOMS
   HYDROGEN-ATOM
   SYSTEMS
Аннотация: We investigate theoretically the dynamics of squeezed state generation in nonlinear systems possessing a transition from regular to chaotic dynamics in the limit of a large number of photons. As an example, the model of a kicked Kerr oscillator is considered. We show that at the transition to quantum chaos the maximum possible degree of squeezing increases exponentially in time, in contrast to the regular dynamics, where the degree of squeezing increases only powerwise in time. We demonstrate the one-to-one correspondence of the degree of squeezing and the value of the local Lyapunov instability rate in the corresponding classical chaotic system.

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Держатели документа:
Abo Akad, Dept Phys, SF-20500 Turku, Finland
Russian Acad Sci, LV Kirensky Phys Inst, Theory Nonlinear Proc Lab, Krasnoyarsk 660036, Russia
Palacky Univ, Dept Opt, Olomouc 77207, Czech Republic
Palacky Univ, Joint Lab Opt, Olomouc 77207, Czech Republic
ИФ СО РАН

Доп.точки доступа:
Perina, J.
}
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10.

Gluck, M.
Bloch particle in the presence of dc and ac fields / M. . Gluck, A. R. Kolovsky, H. J. Korsch // Phys. Lett. A. - 1998. - Vol. 249, Is. 5-6. - P. 483-488, DOI 10.1016/S0375-9601(98)00763-4. - Cited References: 21 . - ISSN 0375-9601

РУБ Physics, Multidisciplinary
Рубрики:
DYNAMIC LOCALIZATION
ELECTRONS
ATOMS
Кл.слова (ненормированные):
Wannier-Bloch states -- quantum chaos
Аннотация: In this Letter we study the metastable states of a Bloch particle in the presence of external ac and de fields. For the resonance condition between the period of the driving frequency and the Bloch period, the complex quasi-energies are numerically calculated for two qualitatively different regimes (quasi-regular and chaotic) of the system dynamics. For the chaotic regime an effect of quantum stabilization, which suppresses the classical decay mechanism, is found. This effect is demonstrated to be a kind of quantum phenomenon sensitive to the resonance condition. (C) 1998 Elsevier Science B.V.

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Держатели документа:
Univ Kaiserslautern, Fachbereich Phys, D-67653 Kaiserslautern, Germany
LV Kirensky Phys Inst, Krasnoyarsk 660036, Russia
ИФ СО РАН
Fachbereich 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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11.

Quantum nonlinear resonance and quantum chaos in Aharonov-Bohm oscillations in mesoscopic semiconductor rings / G. P. Berman [et al.] // Phys. Rev. B. - 1997. - Vol. 56, Is. 16. - P. 10338-10354, DOI 10.1103/PhysRevB.56.10338. - Cited References: 51 . - ISSN 0163-1829

РУБ Physics, Condensed Matter
Рубрики:
EXCITED HYDROGEN-ATOMS
   FREQUENCY ELECTROMAGNETIC-FIELD
   PERSISTENT CURRENTS
   NORMAL-METAL
   ENERGY SPACE
   LOCALIZATION
   TRANSPORT
   LOOP
   TIME
   TRANSMISSION
Аннотация: We consider Aharonov-Bohm oscillations in a mesoscopic semiconductor ring threaded by both a constant magnetic flux and a time-dependent, resonant magnetic field with one or two frequencies. Working in the ballistic regime, we establish that the theory of ''quantum nonlinear resonance'' applies, and thus that this system represents a possible solid-state realization of ''quantum nonlinear resonance'' and ''quantum chaos.'' In particular, we investigate the behavior of the time-averaged electron energy at zero temperature in the regimes of (i) an isolated quantum nonlinear resonance and (ii) the transition to quantum chaos, when two quantum nonlinear resonances overlap. The time-averaged energy exhibits sharp resonant behavior as a function of the applied constant magnetic flux, and has a staircase dependence on the amplitude of the external time-dependent field. In the chaotic regime, the resonant behavior exhibits complex structure as a function of flux and frequency. We compare and contrast the quantum chaos expected in these mesoscopic ''solid-state atoms'' with that observed in Rydberg atoms in microwave fields, and discuss the prospects for experimental observation of the effects we predict.

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Держатели документа:
LOS ALAMOS NATL LAB,CTR NONLINEAR STUDIES,LOS ALAMOS,NM 87545
LV KIRENSKII INST PHYS,KRASNOYARSK 660036,RUSSIA
UNIV ILLINOIS,DEPT PHYS,URBANA,IL 61801
UKRAINIAN ACAD SCI,INST LOW TEMP PHYS & ENGN,UA-310164 KHARKOV,UKRAINE
ИФ СО РАН

Доп.точки доступа:
Berman, G. P.; Bulgakov, E. N.; Булгаков, Евгений Николаевич; Campbell, D. K.; Krive, I. V.
}
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12.

Alekseev, K. N.
Squeezed states and quantum chaos / K. N. Alekseev, D. S. Priimak // J. Exp. Theor. Phys. - 1998. - Vol. 86, Is. 1. - P. 61-70, DOI 10.1134/1.558469. - Cited References: 41 . - ISSN 1063-7761

РУБ Physics, Multidisciplinary
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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Держатели документа:
Russian Acad Sci, LV Kirensky Phys Inst, Siberian Branch, Krasnoyarsk 660036, Russia
ИФ СО РАН

Доп.точки доступа:
Priimak, D. S.
}
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13.

Kolovsky, A. R.
Relativistic chaos for an electron in a standing microwave field / A. R. Kolovsky // Europhys. Lett. - 1998. - Vol. 41, Is. 3. - P. 257-260, DOI 10.1209/epl/i1998-00139-0. - Cited References: 9 . - ISSN 0295-5075

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

Доп.точки доступа:
Коловский, Андрей Радиевич
}
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14.

Structural heterogeneity detonation diamond-containing mate rial [Text] / A. Ya. Korets, A. S. Krylov, E. V. Mironov // 3rd Chaotic modeling and Simulation International Conference: CHAOS 2010. - 2010. - P34

Доп.точки доступа:
Korets, A.Ya.; Krylov, A.S.; Mironov, E.V.; Chaotic modeling and Simulation International Conference(2010 ; Jun/ ; 1-4 ; Chania, Crete, Greece)
}
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15.

    Kolovsky, A. R.
    Evaporative Cooling and Self-Thermalization in an Open System of Interacting Fermions / A. R. Kolovsky, D. L. Shepelyansky // Ann. Phys.-Berlin. - 2019. - Vol. 531, Is. 12. - Ст. 1900231, DOI 10.1002/andp.201900231. - Cited References: 24. - For D.L.S. this work was supported in part by the Programme Investissements d'Avenir ANR-11-IDEX-0002-02, reference ANR-10-LABX-0037-NEXT (project THETRACOM). For A.R.K. this work was supported in part by Russian Science Foundation through the grant N19-12-00167. . - ISSN 0003-3804. - ISSN 1521-3889
   Перевод заглавия: Испарительное охлаждение и само-термализация в открытой системе взаимодействующих фермионов
Рубрики:
QUANTUM CHAOS
   DISTRIBUTIONS
   STATISTICS
Кл.слова (ненормированные):
open quantum systems -- quantum chaos -- self-thermalization
Аннотация: Depletion dynamics of an open system of weakly interacting fermions with two-body random interactions is studied. In this model, fermions are escaping from the high-energy one-particle orbitals, that mimics the evaporation process used in laboratory experiments with neutral atoms to cool them to ultra-low temperatures. It is shown that due to self-thermalization the system instantaneously adjusts to the new temperature which decreases with the course of time.

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Держатели документа:
Kirensky Inst Phys, Krasnoyarsk 660036, Russia.
Siberian Fed Univ, Krasnoyarsk 660041, Russia.
Univ Toulouse, UPS, Lab Phys Theor, IRSAMC,CNRS, F-31062 Toulouse, France

Доп.точки доступа:
Shepelyansky, Dima L.; Коловский, Андрей Радиевич; Programme Investissements d'AvenirFrench National Research Agency (ANR) [ANR-11-IDEX-0002-02, ANR-10-LABX-0037-NEXT]; Russian Science FoundationRussian Science Foundation (RSF) [N19-12-00167]
}
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16.

    Bychek, A. A.
    Probing quantum chaos in many-body quantum systems by the induced dissipation / A. A. Bychek, P. S. Muraev, A. R. Kolovsky // Phys. Rev. A. - 2019. - Vol. 100, Is. 1. - Ст. 013610, DOI 10.1103/PhysRevA.100.013610. - Cited References: 29. - This work has been supported through Russian Science Foundation Grant N19-12-00167. The authors are grateful to D. N. Maksimov for stimulating discussions. . - ISSN 2469-9926. - ISSN 2469-9934
   Перевод заглавия: Исследование квантового хаоса в многочастичных квантовых системах при помощи диссипации

РУБ Optics + Physics, Atomic, Molecular & Chemical

Аннотация: We theoretically analyze the depletion dynamics of an ensemble of cold atoms in a quasi-one-dimensional optical lattice where atoms in one of the lattice sites are subject to decay. Unlike the previous studies of this problem in Labouvie et al., Phys. Rev. Lett. 116, 235302 (2016), we focus on the case where the system is brought to the chaotic regime, which crucially modifies the depletion dynamics as compared to the regular case. It is shown that depletion of the affected site results in gradual depletion of the neighboring sites according to the t1/3 scaling law. We also show that by measuring occupations of the lattice sites one can extract important information on chaotic dynamics of the original conservative system.

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Держатели документа:
Kirensky Inst Phys, Krasnoyarsk 660036, Russia.
Siberian Fed Univ, Krasnoyarsk 660041, Russia.

Доп.точки доступа:
Muraev, Pavel S.; Kolovsky, A. R.; Коловский, Андрей Радиевич; Бычек, Анна Андреевна; Russian Science Foundation [N19-12-00167]
}
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17.

Muraev, P. S.
Signatures of quantum chaos and fermionization in the incoherent transport of bosonic carriers in the Bose-Hubbard chain / P. S. Muraev, D. N. Maksimov, A. R. Kolovsky // Phys. Rev. E. - 2024. - Vol. 109, Is. 3. - Ст. L032107, DOI 10.1103/PhysRevE.109.L032107. - Cited References: 34. - The authors acknowledge financial support from the Ministry of Science and Higher Education of Russian Federation (Project No. FSRZ-2023-0006) . - ISSN 2470-0045. - ISSN 2470-0053
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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Держатели документа:
Kirensky Institute of Physics, Federal Research Centre KSC SB RAS, 660036 Krasnoyarsk, Russia
School of Engineering Physics and Radio Electronics, Siberian Federal University, 660041 Krasnoyarsk, Russia
IRC SQC, Siberian Federal University, 660041 Krasnoyarsk, Russia

Доп.точки доступа:
Maksimov, D. N.; Максимов, Дмитрий Николаевич; Kolovsky, A. R.; Коловский, Андрей Радиевич; Мураев, Павел Сергеевич
}
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18.

Quantum Chaos, Transport, and Control-in Quantum Optics [Text] / J. Madronero [et al.] // Advances in Atomic, Molecular and Optical Physics. - 2006. - Vol. 53. - P. 33-73, DOI 10.1016/S1049-250X(06)53002-2 . - ISSN 1049-250X

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Держатели документа:
Arnold-Sommerfeld-Zentrum fur Theoretische Physik,Ludwig-Maximilians-Universitat Munchen
Dipartimento di Fisica Enrico Fermi,CNR-INFM,Universita di Pisa
Max-Planck-Institut fur Physik komplexer Systeme
Physik Department,Technische Universitat Munchen
Theoretische Physik,Universitat Regensburg

Доп.точки доступа:
Madronero, J.; Schlagheck, P.; Ponomarev, A.; Carvalho, A.R.R.; Viviescas, C.; Kolovsky, A. R.; Krug, A.; Buchleitner, A.; Wimberger, S.; Hornberger, K.
}
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19.

Kolovsky, A. R.
Bistability and chaos-assisted tunneling in dissipative quantum systems / A. R. Kolovsky // Phys. Rev. E. - 2022. - Vol. 106, Is. 1. - Ст. 014209, DOI 10.1103/PhysRevE.106.014209. - Cited References: 21. - The author acknowledges financial support from the Russian Science Foundation through Grant No. 19-12-00167 . - ISSN 2470-0045
Кл.слова (ненормированные):
Bi-stability -- Chaos-assisted tunneling -- Dissipative quantum systems -- Double resonance -- Driving frequencies -- Limit-cycle -- Multistability -- Non-linear oscillators -- Quantum limit -- Resonance model
Аннотация: We revisit the problem of quantum bi- and multistability by considering the dissipative double resonance model. For a large driving frequency, this system has a simpler phase structure than the driven dissipative nonlinear oscillator, the paradigm model for classical and quantum bistability. This allows us to obtain an analytical estimate for the lifetime of quantum limit cycles. On the other hand, for a small driving frequency, the system is much richer than the nonlinear oscillator. This allows us to address a novel phenomenon of dissipation- and chaos-assisted tunneling between quantum limits cycles.

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Держатели документа:
Siberian Federal University, Krasnoyarsk, 660041, Russian Federation
Kirensky Institute of Physics, Krasnoyarsk, 660036, Russian Federation

Доп.точки доступа:
Коловский, Андрей Радиевич
}
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20.

Order and chaos in classical spin chain models / P. I. Belobrov [et al.] // Zhurnal Eksperimentalnoi Teor. Fiz. - 1984. - Vol. 87, Is. 1. - P. 310-322. - Cited References: 24 . - ISSN 0044-4510

РУБ Physics, Multidisciplinary

WOS
Доп.точки доступа:
Belobrov, P. I.; Белобров, Петр Иванович; Beloshapkin, V. V.; Белошапкин, Валерий Васильевич; Zaslavsky, G. M.; Заславский, Георгий Моисеевич; Tretyakov, A. G.; Третьяков, Александр Григорьевич
}
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