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Вид документа : Статья из журнала
Шифр издания :
Автор(ы) : Bulgakov E. N., Maksimov D. N., Sadreev A. F.
Заглавие : Electric circuit networks equivalent to chaotic quantum billiards
Место публикации : Phys. Rev. E: AMERICAN PHYSICAL SOC, 2005. - Vol. 71, Is. 4. - Ст.46205. - ISSN 1063-651X, DOI 10.1103/PhysRevE.71.046205
Примечания : Cited References: 31
Предметные рубрики: TIME-REVERSAL SYMMETRY
CONDUCTANCE FLUCTUATIONS
STATISTICS
SYSTEMS
EIGENFUNCTIONS
DOTS
Ключевые слова (''Своб.индексиров.''): 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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Вид документа : Статья из журнала
Шифр издания :
Автор(ы) : Maksimov D. N., Sadreev A. F.
Заглавие : Bound states in elastic waveguides
Место публикации : Phys. Rev. E: AMERICAN PHYSICAL SOC, 2006. - Vol. 74, Is. 1. - Ст.16201. - ISSN 1539-3755, DOI 10.1103/PhysRevE.74.016201
Примечания : Cited References: 26
Предметные 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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Вид документа : Статья из журнала
Шифр издания :
Автор(ы) : Maksimov D. N., Sadreev A. F.
Заглавие : Phase correlation function of complex random Gaussian fields
Место публикации : Europhys. Lett. - 2007. - Vol. 80, Is. 5. - Ст.50003. - ISSN 0295-5075, DOI 10.1209/0295-5075/80/50003
Примечания : Cited References: 22
Предметные 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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Вид документа : Статья из журнала
Шифр издания :
Автор(ы) : Maksimov D. N., Sadreev A. F.
Заглавие : Gaussian random waves in elastic media
Место публикации : JETP Letters. - 2007. - Vol. 86, Is. 9. - P.584-588. - ISSN 0021-3640, DOI 10.1134/S0021364007210060
Примечания : Cited References: 22
Предметные 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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Вид документа : Статья из журнала
Шифр издания :
Автор(ы) : Maksimov D. N., Sadreev A. F.
Заглавие : Statistics of nodal points of in-plane random waves in elastic media
Место публикации : Phys. Rev. E: AMER PHYSICAL SOC, 2008. - Vol. 77, Is. 5. - Ст.56204. - ISSN 1539-3755, DOI 10.1103/PhysRevE.77.056204
Примечания : Cited References: 39
Предметные рубрики: PHASE SINGULARITIES
SPECTRAL STATISTICS
FIELDS
BILLIARDS
PATTERNS
Ключевые слова (''Своб.индексиров.''): 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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Вид документа : Статья из журнала
Шифр издания :
Автор(ы) : Berggren K. F., Maksimov D. N., Sadreev A. F., Hohmann R., Kuhl U., Stockmann H. J.
Заглавие : Quantum stress in chaotic billiards
Место публикации : Phys. Rev. E: AMER PHYSICAL SOC, 2008. - Vol. 77, Is. 6. - Ст.66209. - ISSN 1539-3755, DOI 10.1103/PhysRevE.77.066209
Примечания : Cited References: 43
Предметные рубрики: MICROWAVE CAVITIES
WAVE-FUNCTIONS
STATISTICAL PROPERTIES
SYSTEMS
FIELDS
Ключевые слова (''Своб.индексиров.''): 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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Вид документа : Однотомное издание
Шифр издания : В31 рукописный текст
Автор(ы) : Максимов, Дмитрий Николаевич
Заглавие : 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
Выходные данные : Красноярск, 2008
Колич.характеристики :20 с
Коллективы : Российская академия наук, Сибирское отделение РАН, Институт физики им. Л.В. Киренского Сибирского отделения РАН, Тихоокеанский океанологический институт им. В.И. Ильичева ДВО РАН
Примечания : Библиогр.: 19 назв.
ГРНТИ : 29.19.03 + 29.05.15
Предметные рубрики: Динамические системы-- Волны хаотические-- Исследование
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Вид документа : Однотомное издание
Шифр издания : В31/М 17 рукописный текст
Автор(ы) : Максимов, Дмитрий Николаевич
Заглавие : Проявления волнового хаоса в микроволновых упругих и LCR-биллиардах : дис. на соиск. уч. степени канд. физ.-мат. наук : 01.04.07
Выходные данные : Красноярск, 2008
Колич.характеристики :87 с
Коллективы : Российская академия наук, Сибирское отделение РАН, Институт физики им. Л.В. Киренского Сибирского отделения РАН
Примечания : Библиогр.: 92 назв.
ГРНТИ : 29.19.03 + 29.05.15
ББК : В314я031
Экземпляры :ДС(1)
Свободны : ДС(1)
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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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10.

Вид документа : Статья из сборника (однотомник)
Шифр издания :
Автор(ы) : Maksimov D. N., Chesnokov I. Yu., Makarov D. V., Kolovsky A. R.
Заглавие : Landau-zener tunneling in 2d periodic structures in the presense of a gauge field
Коллективы : Euro-Asian Symposium "Trends in MAGnetism": Nanomagnetism
Место публикации : V Euro-Asian simposium "Trend in MAGnetism": Nanomagnetism: abstracts. - Vladivostok: FEFU, 2013. - С. 71. - ISBN 978-5-7444-3124-2
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