Microwave experiments on chaotic billiards

Sridhar, S.; Hogenboom, Daniel O.; Willemsen, Balam A.

doi:10.1007/bf01048844

Cited by 48 publications

(29 citation statements)

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“…Thus first intensity distributions of the electric field strength were measured with the so called perturbation body method [12]. A small metallic body alters the resonance frequency f 0 of the cavity, where according to the Maier-Slater theorem [13] the frequency…”

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confidence: 99%

First Experimental Observation of Superscars in a Pseudointegrable Barrier Billiard

et al. 2006

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With a perturbation body technique intensity distributions of the electric field strength in a flat microwave billiard with a barrier inside up to mode numbers as large as about 700 were measured. A method for the reconstruction of the amplitudes and phases of the electric field strength from those intensity distributions has been developed. Recently predicted superscars have been identified experimentally and -using the well known analogy between the electric field strength and the quantum mechanical wave function in a two-dimensional microwave billiard -their properties determined.PACS numbers: 05.45. Mt, 03.65.Sq, 42.25.Fx Planar polygonal billiards with angles α j = πm j /n j , where m j and n j are co-prime integers, have been studied both classically and quantum mechanically [1]. When m j = 1 the motion in phase space is not restricted to a torus like for integrable systems, but to a surface with a more complicated topology. Accordingly, such planar polygonal billiards are called pseudointegrable. It was established numerically (see [2,3] and refs. therein) that the statistical properties of the eigenvalues of the corresponding quantum systems are intermediate between those of a regular and a chaotic system. The properties of the wave functions of planar polygonal billiards are also intriguing, as they show a strong scarring behavior which can be related to families of periodic orbits [4]. In a plot of eigenfunctions in the barrier billiard scars are clearly distinguishable from non-scarred eigenfunctions. This pronounced scar structure does not disappear at large quantum numbers in contrast to that in chaotic systems [5,6,7]. To stress this difference it is proposed in [4] to call the scars in pseudointegrable systems superscars, an expression used by Heller in his early seminal paper [6] in a different context. The aim of this letter is to report on the experimental investigation of superscars in the barrier billiard. This is a rectangular billiard of area l x · l y which contains an infinitely thin barrier. In the experiment presented here the barrier is placed on the symmetry line x = l x /2 and its length equals l y /2, where l y is the length of the shorter side of the rectangle.In the present work the quantum barrier billiard is simulated by means of a microwave billiard. Microwave billiards are flat cylindrical resonators [8,9]. Below the critical frequency f c = c/2h, where c is the velocity of light and h is the height of the cavity, the electric field is the solution of the scalar Helmholtz equation with Dirichlet boundary conditions. This equation is mathematically equivalent to the Schrödinger equation for a quantum billiard of corresponding shape (see e.g. [8,9]). A is the area of the billiard. Hence, the number of experimentally accessible resonances increases with the area and decreases with the height of the billiard. The resonances can be well resolved, if their widths are small in comparison with the average spacing between adjacent resonances, i.e. a microwave cavity with a high qual...

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First Experimental Observation of Superscars in a Pseudointegrable Barrier Billiard

et al. 2006

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“…A direct physical proof of isospectrality can be obtained by experiments utilizing microwave cavities [6,7] which provide a simple and powerful method of simulating single particle time-independent quantum mechanics in two dimensions. This follows from the fact that under appropriate geometrical constraints, Maxwell's equations in a cavity reduces to the Schrödinger equation of a free particle inside a two dimensional domain of arbitrary shape and topology .…”

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Isospectrality in chaotic billiards

Dhar

Rao

et al. 2003

Phys. Rev. E

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“…Our proposed q1D microwave setup resembles quasi-twodimensional ͑q2D͒, flat microwave cavities already used successfully for quantum chaos studies ͓24͔. Quasi-2D microwave cavities were first used by Stöckmann and Stein ͓36͔,and Sridhar and collaborators ͓39,40͔ for the study of spectral statistics and wave functions ͓3͔. Later, dielectric-loaded q2D cavities were used for the investigation of nonNewtonian orbits ͓14͔ and an experimental test ͓12,13͔ of a predicted ͓11͔ universal correction to the Weyl formula ͓3͔ of ray-splitting systems ͓8-15͔.…”

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confidence: 99%

Ghost orbit spectroscopy

2006

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Direct periodic-orbit expansions of individual spectral eigenvalues is a new direction in quantum mechanics. Using a unitary -matrix theory, we present exact, convergent, integral-free ghost orbit expansions of spectral eigenvalues for a step potential in the tunneling regime. We suggest an experiment to extract ghost orbit information from measured spectra in the tunneling regime (ghost orbit spectroscopy). We contrast our unitary, convergent theory with a recently published nonunitary, divergent theory [Yu. Dabaghian and R. Jensen, Eur. J. Phys. 26, 423 (2005)].

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Microwave experiments on chaotic billiards

Cited by 48 publications

References 10 publications

First Experimental Observation of Superscars in a Pseudointegrable Barrier Billiard

First Experimental Observation of Superscars in a Pseudointegrable Barrier Billiard

Isospectrality in chaotic billiards

Ghost orbit spectroscopy

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