Abstract
Fluctuations in the one-port scattering and normalized impedance matrices in three polygonal and one chaotic time-reversal invariant microwave billiards are experimentally investigated, in several levels of coupling and absorption, at room temperature and at 77 K. The observed distributions of reflection coefficient, phase of the scattering matrix, resistance and reactance exhibit no fingerprint of a given geometry. At low frequencies, the results are consistent with earlier theoretical models by López, Mello and Seligman and by Zheng, Antonsen and Ott, who independently predicted that the scattering fluctuations might be the same for the Wigner and Poisson level spacing distributions in the lossless cavity. The uniqueness of the observed scattering statistics at higher absorption levels is discussed with respect to inherent limitations posed by the experimental technique.
Highlights
Scattering plays a prominent part in the development of physics and engineering
It is interesting to notice that prediction (i) for the cavity with no loss bears a relation to an earlier result reported by López, Mello and Seligman (LMS) in the early 1980’s13, in the context of statistical nuclear physics
As mentioned before, according to the analytic-ergodic ensemble of matrices S = eiθ introduced by LMS13 almost four decades ago, the corresponding phase distribution would be uniquely given by Eq (2) for both Wigner and Poisson spacing distributions
Summary
Scattering plays a prominent part in the development of physics and engineering. In the past few decades, universal properties of chaotic scattering have been vigorously investigated in nuclei[1], ballistic electronic cavities[2] and microwave billiards[3,4]. Microwave billiards enjoy an interesting electromagnetic analogy with two-dimensional quantum wells and offer advantages for experimental tests of predictions based on random matrix theory (RMT) Experiments in these flat resonators were introduced in the early 1990’s as a tool in the study of quantization of classically chaotic systems[5]. For a time-reversal invariant target in the one-port case, two independent approaches have been reported in the past decade, one for the scattering matrix S, the other one for the impedance matrix Z.
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