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    Максимов, Дмитрий Николаевич.
    Проявления волнового хаоса в микроволновых упругих и LCR-биллиардах [Рукопись] : дис. на соиск. уч. степени канд. физ.-мат. наук : 01.04.07 / Д. Н. Максимов ; науч. рук. А. Ф. Садреев ; Рос. акад. наук, Сиб. отд-ние, Ин-т физики им. Л.В. Киренского. - Красноярск, 2008. - 87 с. - Библиогр.: 92 назв. -

ГРНТИ

29.19.03

29.05.15

ББК В314я031

Держатели документа:
Библиотека Института физики им. Л. В. Киренского СО РАН
Доп.точки доступа:
Садреев, Алмаз Фаттахович \науч. рук.\; Sadreev A.F.; Maksimov D. N.; Российская академия наук; Сибирское отделение РАН; Институт физики им. Л.В. Киренского Сибирского отделения РАН
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Landau-Zener tunnelling in 2D periodic structures in the presence of a gauge field: II. Electric breakdown / D. N. Maksimov [et al.] // J. Phys. B. - 2013. - Vol. 46, Is. 14. - Ст. 145302. - P. , DOI 10.1088/0953-4075/46/14/145302. - Cited References: 16. - The authors acknowledge financial support of Russian Academy of Sciences through the SB RAS integration project no. 29 Dynamics of atomic Bose-Einstein condensates in optical lattices and the RFBR project no. 12-02-00094 Tunneling of the macroscopic quantum states. DVM also acknowledges the support of RFBR through grants no. 12-02-90807 and no. 12-02-31416. . - ISSN 0953-4075

РУБ Optics + Physics, Atomic, Molecular & Chemical

Аннотация: We analyse dynamics of a quantum particle in a square lattice in the Hall configuration beyond the single-band approximation. For vanishing gauge (magnetic) field this dynamics is defined by the inter-band Landau-Zener tunnelling, which is responsible for the phenomenon known as the electric breakdown. We show that in the presence of a gauge field this phenomenon is absent, at least, in its common sense. Instead, the Landau-Zener tunnelling leads to the appearance of a finite current which flows in the direction orthogonal to the vector of a potential (electric) field.

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Держатели документа:
LV Kirenskii Inst Phys, Krasnoyarsk 660036, Russia
Siberian Fed Univ, Inst Engn Phys & Radio Elect, Krasnoyarsk 660041, Russia
Ilichev Pacific Oceanol Inst, Vladivostok 690041, Russia

Доп.точки доступа:
Maksimov, D. N.; Максимов, Дмитрий Николаевич; Chesnokov, I. Yu.; Makarov, D. V.; Kolovsky, A. R.; Коловский, Андрей Радиевич
}
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Landau-zener tunneling in 2d periodic structures in the presense of a gauge field / D. N. Maksimov [и др.] // V Euro-Asian simposium "Trend in MAGnetism": Nanomagnetism : abstracts. - Vladivostok : FEFU, 2013 = EASTMag-2013. - P71 . - ISBN 978-5-7444-3124-2

Доп.точки доступа:
Maksimov, D. N.; Максимов, Дмитрий Николаевич; Chesnokov, I. Yu.; Чесноков, Илья Юрьевич; Makarov, D. V.; Макаров Д.В.; Kolovsky, A. R.; Коловский, Андрей Радиевич; Euro-Asian Symposium "Trends in MAGnetism": Nanomagnetism(5 ; 2013 ; Sept. ; 15-21 ; Vladivostok)
}
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    Maksimov, D. N.
    Symmetry breaking in binary chains with nonlinear sites / D. N. Maksimov, A. F. Sadreev // Phys. Rev. E. - 2013. - Vol. 88, Is. 3. - Ст. 032901. - P. , DOI 10.1103/PhysRevE.88.032901 . - ISSN 1539-3755
   Перевод заглавия: Нарушение симметрии в бинарных цепочках с нелинейными узлами
Аннотация: We consider a system of two or four nonlinear sites coupled with binary chain waveguides. When a monochromatic wave is injected into the first (symmetric) propagation channel, the presence of cubic nonlinearity can lead to symmetry breaking, giving rise to emission of antisymmetric wave into the second (antisymmetric) propagation channel of the waveguides. We found that in the case of nonlinear plaquette, there is a domain in the parameter space where neither symmetry-preserving nor symmetry-breaking stable stationary solutions exit. As a result, injection of a monochromatic symmetric wave gives rise to emission of nonsymmetric satellite waves with energies differing from the energy of the incident wave. Thus, the response exhibits nonmonochromatic behavior. В© 2013 American Physical Society.

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Доп.точки доступа:
Sadreev, A. F.; Садреев, Алмаз Фаттахович; Максимов, Дмитрий Николаевич
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Spectrum of localized states in graphene quantum dots and wires / V. V. Zalipaev [et al.] // Phys. Lett. A. - 2013. - Vol. 377, Is. 3-4. - P. 216-221, DOI 10.1016/j.physleta.2012.11.028 . - ISSN 0375-9601
Кл.слова (ненормированные):
Generalized Bohr-Sommerfeld quantization condition -- Graphene -- High-energy eigenstates -- Semiclassical approximation -- Tunneling
Аннотация: We developed semiclassical method and show that any smooth potential in graphene describing elongated a quantum dot or wire may behave as a barrier or as a trapping well or as a double barrier potential, Fabry-Perot structure, for 1D Schrodinger equation. The energy spectrum of quantum wires has been found and compared with numerical simulations. We found that there are two types of localized states, stable and metastable, having finite life time. These life times are calculated, as is the form of the localized wave functions which are exponentially decaying away from the wire in the perpendicular direction. В© 2012 Elsevier B.V. All rights reserved.

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Держатели документа:
Univ Loughborough, Dept Math Sci, Loughborough LE11 3TU, Leics, England
LV Kirenskii Inst Phys, Krasnoyarsk 660036, Russia
Univ Loughborough, Dept Phys, Loughborough LE11 3TU, Leics, England

Доп.точки доступа:
Zalipaev, V. V.; Maksimov, D. N.; Максимов, Дмитрий Николаевич; Linton, C. M.; Kusmartsev, F. V.
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    Maksimov, D. N.
    Escape dynamics of a Bose-Hubbard dimer out of a trap / D. N. Maksimov, A. R. Kolovsky // Phys. Rev. A. - 2014. - Vol. 89, Is. 6. - Ст. 063612, DOI 10.1103/PhysRevA.89.063612. - Cited References: 53. - The authors acknowledge financial support of Russian Academy of Sciences through the SB RAS integration project No. 29 Dynamics of Atomic Bose-Einstein Condensates in Optical Lattices. . - ISSN 1050-2947. - ISSN 1094-1622
   Перевод заглавия: Динамика туннелирования димера Бозе-Хаббарда из потенциальной ямы

РУБ Optics + Physics, Atomic, Molecular & Chemical
Рубрики:
ULTRACOLD GASES
   OPTICAL LATTICE
   QUANTUM
   DECAY
Аннотация: We consider a potential scattering of a Bose-Hubbard dimer in a one-dimensional optical lattice. A numerical approach based on an effective non-Hermitian Hamiltonian has been developed for solving the scattering problem. It allows us to compute the tunneling and dissociation probabilities for an arbitrary shape of the potential barrier and an arbitrary kinetic energy of the dimer. The developed approach has been used to address the problem of two-particle decay out of a trap. In particular, it is shown that the presence of dissociation channels significantly decreases the nonescape probability due to single-particle escape to those channels.

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Держатели документа:
LV Kirenskii Inst Phys, Krasnoyarsk 660036, Russia
Siberian Fed Univ, Krasnoyarsk 660041, Russia

Доп.точки доступа:
Kolovsky, A. R.; Коловский, Андрей Радиевич; Максимов, Дмитрий Николаевич; Russian Academy of Sciences [29]
}
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    Symmetry breaking in open quantum nonlinear systems / A. F. Sadreev [et al.] // Nonlinear phenomena in complex systems: from nano to macro scale : Springer, 2015. - P. 235-252. - (NATO science for peace and security series C: Environmental security)DOI 10.1007/978-94-017-8704-8_17 . - ISBN 978-94-017-8704-8. - ISBN 978-94-017-8703-1
   Перевод заглавия: Нарушение симметрии в открытых квантовых нелинейных системах
Аннотация: We consider symmetry breaking in the simplest open quantum nonlinear systems such as dimer and plaquette of four nonlinear sites coupled with linear tight-binding wires. If the solution is stationary, the total Hilbert space can be projected into the inner states of the dimer or plaquette by the Feshbach procedure. That derives a nonlinear analogue of the Lippmann-Schwinger equation with injected wave as a source. By neglecting radiation shifts the Lippmann-Scwinger equation limits to the coupled mode theory equations widely used in optics. We show three scenarios for the transmission through the nonlinear quantum systems. The first one inherits the linear case and preserves the symmetry. In the second scenario the symmetry is broken because of different intensities at the dimer sites. In the third scenario the intensities at the sites are equaled but phases of complex wave function are different. That results in a vortical power flow between the nonlinear sites similar to the DC Josephson current. We show how the phenomenon of symmetry breaking can used for switching of outputs symmetrically coupled to the quantum dimer . Also we reveal a domain in the parameter space where none of stationary solutions exist. As a result injection of a monochromatic symmetric wave gives rise to emission of nonsymmetric satellite waves with energies different from the energy of the incident wave. Thus, the response exhibits non monochromatic behavior.

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Держатели документа:
Inst Phys, Krasnoyarsk 660036, Russia

Доп.точки доступа:
Sadreev, A. F.; Садреев, Алмаз Фаттахович; Bulgakov, E. N.; Булгаков, Евгений Николаевич; Maksimov, D. N.; Максимов, Дмитрий Николаевич; Pichugin, K. N.; Пичугин, Константин Николаевич
}
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    Maksimov, D. N.
    Wannier-Stark states in double-periodic lattices. II. Two-dimensional lattices / D. N. Maksimov, E. N. Bulgakov, A. R. Kolovsky // Phys. Rev. A. - 2015. - Vol. 91, Is. 5. - Ст. 053632, DOI 10.1103/PhysRevA.91.053632. - Cited References:22. - The authors acknowledge financial support from Russian Foundation for Basic Research through the Project No. 15-02-00463, Wannier-Stark states and Bloch oscillations of a quantum particle in a generic two-dimensional lattice. . - ISSN 1050. - ISSN 1094-1622
   Перевод заглавия: Состояния Ванье-Штарка в альтернантных решётках. 2. Двумерные решётки

РУБ Optics + Physics, Atomic, Molecular & Chemical
Рубрики:
BLOCH OSCILLATIONS
PARTICLE
LADDERS
Аннотация: We analyze the Wannier-Stark spectrum of a quantum particle in tilted two-dimensional lattices with the Bloch spectrum consisting of two subbands, which could be either separated by a finite gap or connected by the Dirac points. For rational orientations of the static field given by an arbitrary superposition of the translation vectors, the spectrum is a ladder of energy bands. We obtain asymptotic expressions for the energy bands in the limit of large and weak static fields and study them numerically for intermediate field strength. We show that the structure of energy bands determines the rate of spreading of localized wave packets, which is the quantity measured in laboratory experiments. It is shown that wave-packet dispersion becomes a fractal function of the field orientation in the long-time regime of ballistic spreading.

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LV Kirenskii Inst Phys, Krasnoyarsk 660036, Russia
Siberian State Aerosp Univ, Krasnoyarsk 660014, Russia
Siberian Fed Univ, Krasnoyarsk 660041, Russia

Доп.точки доступа:
Bulgakov, E. N.; Булгаков, Евгений Николаевич; Kolovsky, A. R.; Коловский, Андрей Радиевич; Максимов, Дмитрий Николаевич; Russian Foundation for Basic Research [15-02-00463]
}
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    Maksimov, D. N.
    Wannier-Stark states in double-periodic lattices. I. One-dimensional lattices / D. N. Maksimov, E. N. Bulgakov, A. R. Kolovsky // Phys. Rev. A. - 2015. - Vol. 91, Is. 5. - Ст. 053631, DOI 10.1103/PhysRevA.91.053631. - Cited References:24. - The authors acknowledge financial support from Russian Foundation for Basic Research through the Project No. 15-02-00463, Wannier-Stark states and Bloch oscillations of a quantum particle in a generic two-dimensional lattice. . - ISSN 1050. - ISSN 1094-1622
   Перевод заглавия: Состояния Ванье-Штарка в альтернантных решётках. 1. Одномерные решётки

РУБ Optics + Physics, Atomic, Molecular & Chemical
Рубрики:
BLOCH-ZENER OSCILLATIONS
   TIGHTLY BOUND ELECTRONS
   BANDS
   FIELD
Аннотация: We analyze the Wannier-Stark spectrum of a quantum particle in generic one-dimensional double-periodic lattices. In the limit of a weak static field, the spectrum is shown to be a superposition of two Wannier-Stark ladders originating from two Bloch subbands. As the strength of the field is increased, the spectrum rearranges itself into a single Wannier-Stark ladder. We derive analytical expressions that describe the rearrangement employing the analogy between the Wannier-Stark problem and a driven two-level system in the strong-coupling regime.

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Держатели документа:
LV Kirenskii Inst Phys, Krasnoyarsk 660036, Russia
Siberian State Aerosp Univ, Krasnoyarsk 660014, Russia
Siberian Fed Univ, Krasnoyarsk 660041, Russia

Доп.точки доступа:
Bulgakov, E. N.; Булгаков, Евгений Николаевич; Kolovsky, A. R.; Коловский, Андрей Радиевич; Максимов, Дмитрий Николаевич; Russian Foundation for Basic Research [15-02-00463]
}
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10.

    Coupled mode theory for acoustic resonators / D. N. Maksimov [et al.] // Wave Motion. - 2015. - Vol. 56. - P. 52-66, DOI 10.1016/j.wavemoti.2015.02.003. - Cited References:42. - We thank K.N. Pichugin for helpful discussions. The work was supported by grant 14-12-00266 from Russian Science Foundation. . - ISSN 0165. - ISSN 1878-433X
   Перевод заглавия: Теория связанных мод для акустических резонаторов
Рубрики:
WAVE-GUIDES
   TRAPPED MODES
   DISCONTINUITIES
   TRANSMISSION
   BILLIARDS
Кл.слова (ненормированные):
Coupled mode theory -- Non-Hermitian Hamiltonian -- Acoustic resonator -- s-matrix
Аннотация: We develop the effective non-Hermitian Hamiltonian approach for open systems with Neumann boundary conditions. The approach can be used for calculating the scattering matrix and the scattering function in open resonator–waveguide systems. In higher than one dimension the method represents acoustic coupled mode theory in which the scattering solution within an open resonator is found in the form of expansion over the eigenmodes of the closed resonator decoupled from the waveguides. The problem of finding the transmission spectra is reduced to solving a set of linear equations with a non-Hermitian matrix whose anti-Hermitian term accounts for coupling between the resonator eigenmodes and the scattering channels of the waveguides. Numerical applications to acoustic two-, and three-dimensional resonator–waveguide problems are considered.

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Держатели документа:
LV Kirenskii Inst Phys, Krasnoyarsk 660036, Russia
Siberian Fed Univ, Krasnoyarsk 660080, Russia

Доп.точки доступа:
Maksimov, D. N.; Максимов, Дмитрий Николаевич; Sadreev, A. F.; Садреев, Алмаз Фаттахович; Lyapina, A. A.; Ляпина, Алина Андреевна; Pilipchuk, A. S.; Пилипчук, Артем Сергеевич; Russian Science Foundation [14-12-00266]
}
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11.

    Sadreev, A. F.
    Gate controlled resonant widths in double-bend waveguides: bound states in the continuum / A. F. Sadreev, D. N. Maksimov, A. S. Pilipchuk // J. Phys.: Condens. Matter. - 2015. - Vol. 27, Is. 29. - Ст. 295303, DOI 10.1088/0953-8984/27/29/295303. - Cited References:52. - This work is supported by the Russian Science Foundation through Grant No. 14-12-00266. AS is grateful K-F Berggren for discussions. . - ISSN 0953. - ISSN 1361-648X
   Перевод заглавия: Управление резонансными ширинами в двух-коленных волноводах: связанные состояния в континууме

РУБ Physics, Condensed Matter
Рубрики:
CIRCULAR BENDS
   NUCLEAR REACTIONS
   FANO RESONANCES
   UNIFIED THEORY
   QUANTUM
   TRANSMISSION
   TRANSPORT
   SYSTEMS
Кл.слова (ненормированные):
double-bent waveguide -- effective non-Hermittian Hamiltonian -- bound -- states in the continuum
Аннотация: We consider quantum transmission through double-bend Pi- and Z-shaped waveguides controlled by the finger gate potential. Using the effective non-Hermitian Hamiltonian approach we explain the resonances in transmission. We show a difference in transmission in the short waveguides that is the result of different chirality in Z and Pi waveguides. We demonstrate that the potential selectively affects the resonant widths resulting in the occurrence of bound states in the continuum.

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Держатели документа:
Russian Acad Sci, Siberian Branch, Kirensky Inst Phys, Krasnoyarsk 660036, Russia.
Siberian Fed Univ, Krasnoyarsk 660080, Russia.

Доп.точки доступа:
Maksimov, D. N.; Максимов, Дмитрий Николаевич; Pilipchuk, A. S.; Пилипчук, Артем Сергеевич; Садреев, Алмаз Фаттахович; Russian Science Foundation [14-12-00266]
}
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12.

    Bound states in the continuum in open acoustic resonators / A. A. Lyapina [et al.] // J. Fluid Mech. - 2015. - Vol. 780. - P. 370-387, DOI 10.1017/jfm.2015.480. - Cited References: 48. - This work has been supported by Russian Science Foundation through grant 14-12-00266. . - ISSN 0022-1120
   Перевод заглавия: Связанное состояние в континууме в открытом акустическом резонаторе

РУБ Mechanics + Physics, Fluids & Plasmas
Рубрики:
TRAPPED MODES
   FANO RESONANCES
   COMPLEX RESONANCES
   PARALLEL PLATES
   SIDE-BRANCHES
   WAVE-GUIDES
   ABSORPTION
   TRANSPORT
   CHANNELS
   SYSTEM
Кл.слова (ненормированные):
aeroacoustics -- noise control -- wave scattering
Аннотация: We consider bound states in the continuum (BSCs) or embedded trapped modes in two- and three-dimensional acoustic axisymmetric duct-cavity structures. We demonstrate numerically that, under variation of the length of the cavity, multiple BSCs occur due to the Friedrich-Wintgen two-mode full destructive interference mechanism. The BSCs are detected by tracing the resonant widths to the points of the collapse of Fano resonances where one of the two resonant modes acquires infinite life-time. It is shown that the approach of the acoustic coupled mode theory cast in the truncated form of a two-mode approximation allows us to analytically predict the BSC frequencies and shape functions to a good accuracy in both two and three dimensions. © 2015 Cambridge University Press.

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

Доп.точки доступа:
Lyapina, A. A.; Ляпина, Алина Андреевна; Maksimov, D. N.; Максимов, Дмитрий Николаевич; Pilipchuk, A. S.; Пилипчук, Артем Сергеевич; Sadreev, A. F.; Садреев, Алмаз Фаттахович
}
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13.

Quantum stress in chaotic billiards / K. F. Berggren [et al.] // Phys. Rev. E. - 2008. - Vol. 77, Is. 6. - Ст. 66209, DOI 10.1103/PhysRevE.77.066209. - Cited References: 43 . - ISSN 1539-3755

РУБ Physics, Fluids & Plasmas + Physics, Mathematical
Рубрики:
MICROWAVE CAVITIES
   WAVE-FUNCTIONS
   STATISTICAL PROPERTIES
   SYSTEMS
   FIELDS
Кл.слова (ненормированные):
Computer networks -- Electric fields -- Electroacupuncture -- Electromagnetic field theory -- Electromagnetic fields -- Electromagnetism -- Function evaluation -- Functions -- Gaussian distribution -- Image segmentation -- Magnetism -- Mathematical models -- Microwaves -- Modal analysis -- Nematic liquid crystals -- Numerical analysis -- Random processes -- Stresses -- Tensors -- Trellis codes -- Two dimensional -- Wave functions -- Waves -- abiotic and biotic stress -- e ,2e theory -- p ,p ,t measurements -- American Physical Society (APS) -- Analytic expressions -- Current flowing -- Dinger equation -- Experimental studies -- Gaussian random fields -- net flows -- Plane waves -- Quantum billiards -- Quantum-mechanical (QM) -- Scattering wave functions -- Sinai billiard (SB) -- Statistical distributions -- Stress tensors -- Two-dimensional (2D) -- Chaotic systems
Аннотация: This paper reports on a joint theoretical and experimental study of the Pauli quantum-mechanical stress tensor T(alpha beta)(x,y) for open two-dimensional chaotic billiards. In the case of a finite current flow through the system the interior wave function is expressed as psi=u + iv. With the assumption that u and v are Gaussian random fields we derive analytic expressions for the statistical distributions for the quantum stress tensor components T(alpha beta). The Gaussian random field model is tested for a Sinai billiard with two opposite leads by analyzing the scattering wave functions obtained numerically from the corresponding Schrodinger equation. Two-dimensional quantum billiards may be emulated from planar microwave analogs. Hence we report on microwave measurements for an open two-dimensional cavity and how the quantum stress tensor analog is extracted from the recorded electric field. The agreement with the theoretical predictions for the distributions for T(alpha beta)(x,y) is quite satisfactory for small net currents. However, a distinct difference between experiments and theory is observed at higher net flow, which could be explained using a Gaussian random field, where the net current was taken into account by an additional plane wave with a preferential direction and amplitude.

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Держатели документа:
[Berggren, Karl-Fredrik
Sadreev, Almas F.] Linkoping Univ, IFM Theory & Modeling, S-58183 Linkoping, Sweden
[Maksimov, Dmitrii N.
Sadreev, Almas F.] LV Kirenskii Inst Phys, Krasnoyarsk 660036, Russia
[Hoehmann, Ruven
Kuhl, Ulrich
Stoeckmann, Hans-Joergen] Univ Marburg, Fachbereich Phys, AG Quantenchaos, D-35032 Marburg, Germany
ИФ СО РАН
IFM-Theory and Modeling, Linkoping University, S-581 83 Linkoping, Sweden
L.V. Kirensky Institute of Physics, Krasnoyarsk 660036, Russian Federation
AG Quantenchaos, Fachbereich Physik der Philipps-Universitat Marburg, Renthof 5, D-35032 Marburg, Germany

Доп.точки доступа:
Berggren, K. F.; Maksimov, D. N.; Максимов, Дмитрий Николаевич; Sadreev, A. F.; Садреев, Алмаз Фаттахович; Hohmann, R.; Kuhl, U.; Stockmann, H. J.
}
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14.

Maksimov, D. N.
Statistics of nodal points of in-plane random waves in elastic media / D. N. Maksimov, A. F. Sadreev // Phys. Rev. E. - 2008. - Vol. 77, Is. 5. - Ст. 56204, DOI 10.1103/PhysRevE.77.056204. - Cited References: 39 . - ISSN 1539-3755

РУБ Physics, Fluids & Plasmas + Physics, Mathematical
Рубрики:
PHASE SINGULARITIES
   SPECTRAL STATISTICS
   FIELDS
   BILLIARDS
   PATTERNS
Кл.слова (ненормированные):
Chaotic systems -- Correlation methods -- Navier Stokes equations -- Random processes -- Statistics -- Elastic media -- In-plane random waves -- Navier-Cauchy equations -- Nodal points (NP) -- Electromagnetic waves
Аннотация: We consider the nodal points (NPs) u=0 and v=0 of the in-plane vectorial displacements u=(u,v) which obey the Navier-Cauchy equation. Similar to the Berry conjecture of quantum chaos, we present the in-plane eigenstates of chaotic billiards as the real part of the superposition of longitudinal and transverse plane waves with random phases. By an average over random phases we derive the mean density and correlation function of NPs. Consequently we consider the distribution of the nearest distances between NPs.

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Держатели документа:
[Maksimov, Dmitrii N.
Sadreev, Almas F.] Russian Acad Sci, Inst Phys, Krasnoyarsk 660036, Russia
ИФ СО РАН
Institute of Physics, Academy of Sciences, 660036 Krasnoyarsk, Russian Federation

Доп.точки доступа:
Sadreev, A. F.; Садреев, Алмаз Фаттахович; Максимов, Дмитрий Николаевич
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15.

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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16.

Maksimov, D. N.
Phase correlation function of complex random Gaussian fields / D. N. Maksimov, A. F. Sadreev // Europhys. Lett. - 2007. - Vol. 80, Is. 5. - Ст. 50003, DOI 10.1209/0295-5075/80/50003. - Cited References: 22 . - ISSN 0295-5075

РУБ Physics, Multidisciplinary
Рубрики:
RANDOM WAVE-FIELDS
QUANTUM DOTS
Аннотация: The phase correlation function exp[i theta(x+s)-i theta(x)] for the complex random Gaussian field psi(x) = vertical bar psi(x)vertical bar exp[i theta(x)] is derived. It is compared to the numerical scattering wave function in the open Sinai billiard. Copyright (C) EPLA, 2007.

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[Sadreev, A. F.] Linkoping Univ, Dept Phys & Measurement Technol, S-58183 Linkoping, Sweden
[Maksimov, D. N.] LV Kirenskii Inst Phys, Krasnoyarsk 660036, Russia
ИФ СО РАН
L.V. Kirensky Institute of Physics, 660036, Krasnoyarsk, Russian Federation
Department of Physics and Measurement Technology, Linkoping University, S-581 83 Linkoping, Sweden

Доп.точки доступа:
Sadreev, A. F.; Садреев, Алмаз Фаттахович; Максимов, Дмитрий Николаевич
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17.

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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18.

Maksimov, D. N.
Bound states in elastic waveguides / D. N. Maksimov, A. F. Sadreev // Phys. Rev. E. - 2006. - Vol. 74, Is. 1. - Ст. 16201, DOI 10.1103/PhysRevE.74.016201. - Cited References: 26 . - ISSN 1539-3755

РУБ Physics, Fluids & Plasmas + Physics, Mathematical
Рубрики:
CLASSICALLY UNBOUND SYSTEM
QUANTUM WIRES
Аннотация: We consider numerically the L-, T-, and X-shaped elastic waveguides with the Dirichlet boundary conditions for in-plane deformations (displacements) which obey the vectorial Navier-Cauchy equation. In the X-shaped waveguide we show the existence of a doubly degenerate bound state with frequency below the first symmetrical cutoff frequency, which belongs to the two-dimensional irreducible representation E of symmetry group C-4v. Moreover the next bound state is below the next antisymmetric cutoff frequency. This bound state belongs to the irreducible representation A(2). The T-shaped waveguide has only one bound state while the L-shaped one has no bound states.

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Держатели документа:
Russian Acad Sci, Inst Phys, Krasnoyarsk 660036, Russia
Linkoping Univ, Dept Phys & Measurement Technol, SE-58183 Linkoping, Sweden
ИФ СО РАН

Доп.точки доступа:
Sadreev, A. F.; Садреев, Алмаз Фаттахович; Максимов, Дмитрий Николаевич
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19.

Tanner, G.
Wave Intensity Distributions in Complex Structures / G. . Tanner, D. J. Chappell, D. N. Maksimov // Acta Phys. Pol. A. - 2011. - Vol. 120, Is. 6A. - P. A172-A177. - Cited References: 19 . - ISSN 0587-4246

РУБ Physics, Multidisciplinary
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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Доп.точки доступа:
Chappell, D. J.; Maksimov, D. N.; Максимов, Дмитрий Николаевич; Workshop on Quantum Chaos and Localisation Phenomena(5 ; 2011 ; May ; 20-22 ; Warsaw)
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20.

Bulgakov, E. N.
Light guiding above the light line in arrays of dielectric nanospheres / E. N. Bulgakov, D. N. Maksimov // Opt. Lett. - 2016. - Vol. 41, Is. 16. - P. 3888-3891, DOI 10.1364/OL.41.003888. - Cited References: 46. - Russian Foundation for Basic Research (RFBR) (16-02-00314). . - ISSN 0146-9592

РУБ Optics
Рубрики:
SUBWAVELENGTH WAVE-GUIDES
   OPTICAL MODES
   NANOPARTICLES
   CHAINS
   RESONANCES
   PARTICLES
   SPHERES
Аннотация: We consider light propagation above the light line in arrays of spherical dielectric nanoparticles. It is demonstrated numerically that quasi-bound leaky modes of the array can propagate both stationary waves and light pulses to a distance of 60 wavelengths at the frequencies close to the bound states in the radiation continuum. A semi-analytical estimate for decay rates of the guided waves is found to match the numerical data to a good accuracy. © 2016 Optical Society of America.

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

Доп.точки доступа:
Maksimov, D. N.; Максимов, Дмитрий Николаевич; Булгаков, Евгений Николаевич
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