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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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11.

Вид документа : Статья из журнала
Шифр издания :
Автор(ы) : Maksimov D. N., Chesnokov I. Yu., Makarov D. V., Kolovsky A. R.
Заглавие : Landau-Zener tunnelling in 2D periodic structures in the presence of a gauge field: II. Electric breakdown
Место публикации : J. Phys. B. - 2013. - Vol. 46, Is. 14. - Ст.145302. - P. - ISSN 0953-4075, DOI 10.1088/0953-4075/46/14/145302
Примечания : 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.
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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12.

Вид документа : Статья из журнала
Шифр издания :
Автор(ы) : Zalipaev V. V., Maksimov D. N., Linton C. M., Kusmartsev F. V.
Заглавие : Spectrum of localized states in graphene quantum dots and wires
Место публикации : Phys. Lett. A. - 2013. - Vol. 377, Is. 3-4. - P.216-221. - ISSN 0375-9601, DOI 10.1016/j.physleta.2012.11.028
Ключевые слова (''Своб.индексиров.''): 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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13.

Вид документа : Статья из журнала
Шифр издания :
Автор(ы) : Maksimov D. N., Sadreev A. F.
Заглавие : Symmetry breaking in binary chains with nonlinear sites
Место публикации : Phys. Rev. E. - 2013. - Vol. 88, Is. 3. - Ст.032901. - P. - ISSN 1539-3755, DOI 10.1103/PhysRevE.88.032901
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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14.

Вид документа : Статья из журнала
Шифр издания :
Автор(ы) : Maksimov D. N., Kolovsky A. R.
Заглавие : Escape dynamics of a Bose-Hubbard dimer out of a trap
Коллективы : Russian Academy of Sciences [29]
Место публикации : Phys. Rev. A: American Physical Society, 2014. - Vol. 89, Is. 6. - Ст.063612. - ISSN 1050-2947, DOI 10.1103/PhysRevA.89.063612. - ISSN 1094-1622
Примечания : 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.
Предметные 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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15.

Вид документа : Статья из журнала
Шифр издания :
Автор(ы) : Maksimov D. N., Bulgakov E. N., Kolovsky A. R.
Заглавие : Wannier-Stark states in double-periodic lattices. I. One-dimensional lattices
Коллективы : Russian Foundation for Basic Research [15-02-00463]
Место публикации : Phys. Rev. A: American Physical Society, 2015. - Vol. 91, Is. 5. - Ст.053631. - ISSN 1050, DOI 10.1103/PhysRevA.91.053631. - ISSN 10941622(eISSN)
Примечания : 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.
Предметные 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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16.

Вид документа : Статья из журнала
Шифр издания :
Автор(ы) : Maksimov D. N., Bulgakov E. N., Kolovsky A. R.
Заглавие : Wannier-Stark states in double-periodic lattices. II. Two-dimensional lattices
Коллективы : Russian Foundation for Basic Research [15-02-00463]
Место публикации : Phys. Rev. A: American Physical Society, 2015. - Vol. 91, Is. 5. - Ст.053632. - ISSN 1050, DOI 10.1103/PhysRevA.91.053632. - ISSN 10941622(eISSN)
Примечания : 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.
Предметные 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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17.

Вид документа : Статья из сборника (однотомник)
Шифр издания :
Автор(ы) : Sadreev A. F., Bulgakov E. N., Maksimov D. N., Pichugin K. N.
Заглавие : Symmetry breaking in open quantum nonlinear systems
Место публикации : 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
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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18.

Вид документа : Статья из журнала
Шифр издания :
Автор(ы) : Lyapina A. A., Maksimov D. N., Pilipchuk A. S., Sadreev A. F.
Заглавие : Bound states in the continuum in open acoustic resonators
Место публикации : J. Fluid Mech. - 2015. - Vol. 780. - P.370-387. - ISSN 0022-1120, DOI 10.1017/jfm.2015.480
Примечания : Cited References: 48. - This work has been supported by Russian Science Foundation through grant 14-12-00266.
Предметные рубрики: TRAPPED MODES
FANO RESONANCES
COMPLEX RESONANCES
PARALLEL PLATES
SIDE-BRANCHES
WAVE-GUIDES
ABSORPTION
TRANSPORT
CHANNELS
SYSTEM
Ключевые слова (''Своб.индексиров.''): 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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19.

Вид документа : Статья из журнала
Шифр издания :
Автор(ы) : Sadreev A. F., Maksimov D. N., Pilipchuk A. S.
Заглавие : Gate controlled resonant widths in double-bend waveguides: bound states in the continuum
Коллективы : Russian Science Foundation [14-12-00266]
Место публикации : J. Phys.: Condens. Matter: IOP Publishing, 2015. - Vol. 27, Is. 29. - Ст.295303. - ISSN 0953, DOI 10.1088/0953-8984/27/29/295303. - ISSN 1361648X(eISSN)
Примечания : 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.
Предметные рубрики: CIRCULAR BENDS
NUCLEAR REACTIONS
FANO RESONANCES
UNIFIED THEORY
QUANTUM
TRANSMISSION
TRANSPORT
SYSTEMS
Ключевые слова (''Своб.индексиров.''): 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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20.

Вид документа : Статья из журнала
Шифр издания :
Автор(ы) : Maksimov D. N., Sadreev A. F., Lyapina A. A., Pilipchuk A. S.
Заглавие : Coupled mode theory for acoustic resonators
Коллективы : Russian Science Foundation [14-12-00266]
Место публикации : Wave Motion: Elsevier Science, 2015. - Vol. 56. - P.52-66. - ISSN 0165, DOI 10.1016/j.wavemoti.2015.02.003. - ISSN 1878433X(eISSN)
Примечания : Cited References:42. - We thank K.N. Pichugin for helpful discussions. The work was supported by grant 14-12-00266 from Russian Science Foundation.
Предметные рубрики: WAVE-GUIDES
TRAPPED MODES
DISCONTINUITIES
TRANSMISSION
BILLIARDS
Ключевые слова (''Своб.индексиров.''): 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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