Ultrasound Resonances in a Rectangular Plate Described by Random Matrices

Schaadt, K.; Simon, Gábor; Ellegaard, C.

doi:10.1238/physica.topical.090a00231

Cited by 9 publications

(14 citation statements)

References 3 publications

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“…In the elastic case spectral statistics coinciding with RMT has been observed in experiments for rectangular and stadium shaped plates [13,14,15]. Recently, spectra of graphs have also be shown to behave quite similar to chaotic systems [16,17]; they posses a trace formula for the spectral density and show random matrix statistics.…”

Section: Introductionmentioning

confidence: 73%

“…This regime calls for a more refined approximation of the Bessel functions occurring in the traction matrix (15) as for example uniform approximations. Furthermore, periodic orbits accumulate at the boundary and the stationary phase approximation used to solve the integrals (35) breaks down.…”

Section: Summary and Discussionmentioning

confidence: 99%

“…The traction matrices t ± are obtained from (15) by replacing the Bessel functions in terms of outgoing and incoming Hankel…”

Section: B2 the High Frequency Limitmentioning

confidence: 99%

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Wave chaos in the elastic disk

Søndergaard

Tanner

2002

Phys. Rev. E

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The relation between the elastic wave equation for plane, isotropic bodies and an underlying classical ray dynamics is investigated. We study in particular the eigenfrequencies of an elastic disc with free boundaries and their connection to periodic rays inside the circular domain. Even though the problem is separable, wave mixing between the shear and pressure component of the wave field at the boundary leads to an effective stochastic part in the ray dynamics. This introduces phenomena typically associated with classical chaos as for example an exponential increase in the number of periodic orbits. Classically, the problem can be decomposed into an integrable part and a simple binary Markov process. Similarly, the wave equation can in the high frequency limit be mapped onto a quantum graph. Implications of this result for the level statistics are discussed. Furthermore, a periodic trace formula is derived from the scattering matrix based on the inside-outside duality between eigen-modes and scattering solutions and periodic orbits are identified by Fourier transforming the spectral density.

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Section: Introductionmentioning

confidence: 73%

Section: Summary and Discussionmentioning

confidence: 99%

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Wave chaos in the elastic disk

Søndergaard

Tanner

2002

Phys. Rev. E

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“…The statistics of the squared amplitudes (the probability density for the case of quantum billiard) then obeys the Porter-Thomas distribution [2] as described by the Gaussian orthogonal ensemble (GOE). This kind of statistic has been observed experimentally for microwave cavities [3,4] and acoustic resonators [5,6]. These general observations do not apply to wave functions that are scarred along unstable periodic orbits, or show regular patterns associated with bouncing ball motion [7].…”

Section: Introductionmentioning

confidence: 88%

Current statistics for wave transmission through an open Sinai billiard: Effects of net currents

Sadreev

Berggren

2004

Phys. Rev. E

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Transport through quantum and microwave cavities is studied by analytic and numerical techniques. In particular, we consider the statistics for a finite net probability current (Poynting vector) ͗j͘ flowing through an open ballistic Sinai billiard to which two opposite leads/wave guides are attached. We show that if the net probability current is small, the scattering wave function inside the billiard is well approximated by a Gaussian random complex field. In this case, the current statistics are universal and obey simple analytic forms. For larger net currents, these forms still apply over several orders of magnitudes. However, small characteristic deviations appear in the tail regions. Although the focus is on electron and microwave billiards, the analysis is relevant also to other classical wave cavities as, for example, open planar acoustic reverberation rooms, elastic membranes, and water surface waves in irregularly shaped vessels.

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“…The Sinai billiard [13] and Bunimovich stadium [14] are examples of chaotic systems, whereas the circle and the rectangle are integrable. Those billiards have been extensively studied theoretically [15], numerically [4,[16][17][18][19][20], and experimentally [11,21,22].…”

Section: Introductionmentioning

confidence: 99%

Deviations from Poisson statistics in the spectra of free rectangular thin plates

López-González,

Franco-Villafañe,

Méndez-Sánchez

et al. 2021

Preprint

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Ultrasound Resonances in a Rectangular Plate Described by Random Matrices

Cited by 9 publications

References 3 publications

Wave chaos in the elastic disk

Wave chaos in the elastic disk

Current statistics for wave transmission through an open Sinai billiard: Effects of net currents

Deviations from Poisson statistics in the spectra of free rectangular thin plates

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