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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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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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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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Держатели документа:
[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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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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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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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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   В31

    Максимов, Дмитрий Николаевич.
    Проявления волнового хаоса в микроволновых упругих и LCR-биллиардах : автореферат дис. на соиск. уч. степени канд. физ.-мат. наук : 01.04.07 : защищена 24.10.2008 / Д. Н. Максимов ; науч. рук. А. Ф. Садреев ; офиц. опп.: В. М. Логинов, Д. М. Дзебисашвили ; Рос. акад. наук, Сиб. отд-ние, Ин-т физики им. Л.В. Киренского, вед. орг. Тихоокеан. океаногр. ин-т им. В.И. Ильичева. - Красноярск, 2008. - 20 с. - Библиогр.: 19 назв. -

ГРНТИ

29.19.03

29.05.15

Рубрики:
Динамические системы--Волны хаотические--Исследование

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Держатели документа:
Институт физики им. Л.В. Киренского СО РАН

Доп.точки доступа:
Садреев, Алмаз Фаттахович \науч. рук.\; Sadreev, A. F.; Логинов, Валерий Михайлович \офиц. опп.\; Дзебисашвили, Дмитрий Михайлович \офиц. опп.\; Dzebisashvili, D. M.; Maksimov, D. N.; Российская академия наук; Сибирское отделение РАН; Институт физики им. Л.В. Киренского Сибирского отделения РАН; Тихоокеанский океанологический институт им. В.И. Ильичева ДВО РАН
Свободных экз. нет}
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   В31
   М 17

    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
Экземпляры всего: 1
ДС (1)
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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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10.

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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