Experimental and Numerical Studies of One-Dimensional and Three-Dimensional Chaotic Open Systems

Abstract

We present the results of experimental studies of microwave irregular networks and a three-dimensional microwave rough cavity in the presence of absorption. Microwave networks are also analyzed numerically. Microwave networks simulate one-dimensional quantum graphs. The networks consist of coaxial cables connected by joints and attenuators to control absorption. Three-dimensional microwave rough cavities have no formal analog in quantum 3D systems. However, some statistical properties of their spectra such as the level spacing distribution confirms that they belong to the wave-chaotic systems. Absorption of the cavity was changed by using a foam microwave absorber.

Experimental and Numerical Study of Spectral Properties of Three-Dimensional Chaotic Microwave Cavities: The Case of Missing Levels

“…The "third" empty hole was plugged by brass plug during the measurement. Previous measurements [23] have shown that the total absorption of the cavity is mainly related to internal absorption much greater than that associated with antennas/channels.…”

“…Thus, the cavities cannot simulate quantum systems. Nevertheless, the spectral statistics of irregular/rough 3D cavities display behavior characteristic for classically chaotic quantum systems [16][17][18][19][20][21][22][23][24].…”

Missing-level statistics and analysis of the power spectrum of level fluctuations of three-dimensional chaotic microwave cavities

“…The resonance frequencies of the cavity were obtained from the elements S 11 , S 22 , and The distribution of the reflection coefficient P (R) [25] revealed that the total absorption of the measured system is dominated by the internal absorption of the cavity, which is roughly 3 times larger than the absorption introduced by a single antenna. GHz, respectively.…”

“…[16,17]. In the presence of strong absorption the experimental distribution P (R) of the reflection coefficient R for the 3D microwave rough cavity was measured by Lawniczak et al [25] while the impedance and scattering variance ratios were evaluated by Yeh et al [26] in the 3D microwave reverberating cavity. In both cases the experimental results appeared to be in good agreement with the Random Matrix Theory (RMT) predictions.…”