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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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Kolovsky, A. R.
Bogoliubov depletion of the fragmented condensate in the bosonic flux ladder / A. R. Kolovsky // Phys. Rev. A. - 2017. - Vol. 95, Is. 3. - Ст. 033622, DOI 10.1103/PhysRevA.95.033622. - Cited References: 31. - The author acknowledges discussions with A. Eckardt, the hospitality of MPIPKS in Dresden, and financial support from Russian Foundation for Basic Research, Government of Krasnoyarsk Territory, and Krasnoyarsk Region Science and Technology Support Fund through Grant No. 16-42-240746. . - ISSN 1050-2947
Кл.слова (ненормированные):
Bosons -- Crystal lattices -- Ladders -- Optical lattices -- Bogoliubov -- Dispersion relations -- Interacting bosons -- Ultracold atoms -- Ground state
Аннотация: We theoretically analyze the ground state of weakly interacting bosons in the flux ladder - the system that has been recently realized by means of ultracold atoms in the specially designed optical lattice [M. Atala, M. Aidelsburger, M. Lohse, J. T. Barreiro, B. Paredes, and I. Bloch, Nat. Phys. 10, 588 (2014)1745-247310.1038/nphys2998]. It is argued that, for the system parameters corresponding to two degenerate minima in the Bloch dispersion relation, the ground state is a fragmented condensate. We study the Bogoliubov depletion of this condensate and discuss the role of boundary conditions. © 2017 American Physical Society.

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

Доп.точки доступа:
Коловский, Андрей Радиевич
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    Bloch oscillations of Bose-Einstein condensates: Quantum counterpart of dynamical instability / A. R. Kolovsky, H. J. Korsch, E. M. Graefe // Phys. Rev. A. - 2009. - Vol. 80, Is. 2, DOI 10.1103/PhysRevA.80.023617. - Cited Reference Count: 35. - Гранты: We thank D. Witthaut and F. Trimborn for valuable comments. Support from the Deutsche Forschungsgemeinschaft via the Graduiertenkolleg "Nichtlineare Optik und Ultrakurzzeitphysik" is gratefully acknowledged. - Финансирующая организация: Deutsche Forschungsgemeinschaft . - ISSN 1050-2947
Рубрики:
OPTICAL LATTICE
   ATOMS
Кл.слова (ненормированные):
Bloch dynamics -- Bloch oscillations -- Bogoliubov -- Bose-Einstein condensates -- Chaotic dynamics -- Cold atoms -- Decoherence -- Dinger equation -- Dynamical instabilities -- Equipartition -- Hubbard -- Mean-field -- Optical lattices -- Quantum counterpart -- Quasi-one-dimensional -- Quasimomentum -- Bose-Einstein condensation -- Hamiltonians -- Nonlinear equations -- Steam condensers -- Stability
Аннотация: We study the Bloch dynamics of a quasi-one-dimensional Bose-Einstein condensate of cold atoms in a tilted optical lattice modeled by a Hamiltonian of Bose-Hubbard type. The corresponding mean-field system described by a discrete nonlinear Schrodinger equation can exhibit dynamical (or modulation) instability due to chaotic dynamics and equipartition over the quasimomentum modes. It is shown that these phenomena are related to Bogoliubov's depletion of the Bose-Einstein condensate and a decoherence of the condensate in the many-particle description. Three types of dynamics are distinguished: (i) decaying oscillations in the region of dynamical instability and (ii) persisting Bloch oscillations or (iii) periodic decay and revivals in the region of stability.

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Держатели документа:
LV Kirenskii Inst Phys, Krasnoyarsk 660036, Russia
Siberian Fed Univ, Krasnoyarsk 660036, Russia
Tech Univ Kaiserslautern, Fachbereich Phys, D-67653 Kaiserslautern, Germany

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