We quantify the presence of direct processes in the S matrix of chaotic microwave cavities with absorption in the one-channel case. To this end the full distribution P(S)(S) of the S matrix, i.e., S=sqrt[R]e(itheta), is studied in cavities with time-reversal symmetry for different antenna coupling strengths T(a) or direct processes. The experimental results are compared with random-matrix calculations and with numerical simulations including absorption. The theoretical result is a generalization of the Poisson kernel. The experimental and the numerical distributions are in excellent agreement with theoretical predictions for all cases.
The distribution of reflection coefficients P (R) for chaotic microwave cavities with time-reversal symmetry is investigated in different absorption and antenna coupling regimes. For all regimes the agreement between experimental distributions and random-matrix theory predictions is very good, provided both the antenna coupling Ta and the wall absorption strength Tw are taken into account in an appropriate way. These parameters are determined by independent experimental quantities.PACS numbers: 42.25. Bs, 03.65.Nk, Wave scattering by chaotic and weak disordered systems has motivated a rather intensive research activity. The subject is common to several areas of physics, ranging from nuclear, atomic, molecular, and mesoscopic physics to classical wave scattering, like microwaves, sound, and light (see Refs. [1, 2] for a review). The striking feature shared by all such systems, provided they have a chaotic underlying classical dynamics, is that they show universal transmission fluctuations. These fluctuations are successfully described by random-matrix theory [3,4]. Very recently a comprehensive treatment of absorption, ubiquitous in experiments, was developed for systems without time-reversal symmetry (TRI) [5,6]. For systems with TRI, however, there is a rigorous theory only in limiting cases [5].An analytical expression for the distribution P (R) of the reflection coefficient R in the presence of absorption was derived for an arbitrary number of open channels in the weak absorption limit [7]. In the strong absorption limit P (R) reduces to a simple exponential [8]. In these two works perfect coupling between the channels and the scattering region is assumed. Furthermore, non-resonant backscattering processes [9,10,11], which are present in most experimental situations, have been until now often neglected in cases that absorption is taken into account. It is noteworthy that only few of these works are experimental [12,13,14].The purpose of this letter is to present experimental evidence that random-matrix theory provides a quantitative understanding of the universal reflection fluctuations in chaotic systems. More specifically, we show that this can only be achieved if both the coupling, so far mostly overlooked, and absorption strengths are properly taken into account. To this end we measure P (R) in microwave cavities from weak to strong absorption regimes. A quantitative agreement between experiment and theory is observed for all the cases we have studied. This is remarkable since all theoretical parameters are directly obtained from averaged experimental quantities and not from a fit of P (R) to the data.To study the dependence of P (R) on absorption and coupling strengths, we used three different flat microwaves cavities and measured the reflection. For the half Sinai billiard, Fig. 1(left), 57 reflection spectra were measured by sliding the half circular inset along the wall over 28.5 cm in steps of 0.5 cm. This is a practical way to improve the statistics, notwithstanding the correlations among spectra. F...
To measure and detect elastic waves in metallic rods a low-frequency electromagnetic-acoustic transducer has been developed. Frequencies range from a few hertz up to hundreds of kilohertz. With appropriate configuration of the transducer, compressional or torsional waves can be selectively excited or detected. Although the transducer can be used in many different situations, it has been tested and applied to a locally periodic rod, which consists of a finite number of unit cells. The measured wave amplitudes are compared with theoretical ones, obtained with the one-dimensional transfer matrix method, and excellent agreement is obtained.
The optical analogues of Bloch oscillations and their associated Wannier-Stark ladders have been recently analyzed. In this paper we propose an elastic realization of these ladders, employing for this purpose the torsional vibrations of specially designed one-dimensional elastic systems. We have measured, for the first time, the ladder wave amplitudes, which are not directly accessible either in the quantum mechanical or optical cases. The wave amplitudes are spatially localized and coincide rather well with theoretically predicted amplitudes. The rods we analyze can be used to localize different frequencies in different parts of the elastic systems and viceversa. PACS numbers: 43.35.+d,63.20.Pw,43.40.Cw Recently, undulatory systems showing analogues of Bloch oscillations and Wannier-Stark ladders (WSL) attracted increasing attention in several fields of physics [1,2,3,4,5]. As shown by Bloch, electrons in a periodic potential have extended solutions. The same is true for the behavior of an electron under the action of a static electric field. In contrast, and opposite to intuition, when both the periodic potential and the electric field are present, the solutions are localized; this is only true when band to band Zener tunneling is negligible or the system is short enough. The spectrum then shows equally spaced resonances known as Wannier-Stark ladders, the nearest-neighbor level spacing being proportional to the intensity of the external field [6]. In the time domain, the Wannier-Stark ladders yield the so called Bloch oscillations which consist in a counterintuitive effect where the electrons show an * Permanent address:
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