Statistical properties of the eigenfrequency distribution of three-dimensional microwave cavities

Abstract

We measured the transmission spectra of asymmetrically shaped three-dimensional (3D) microwave cavities to determine resonant frequencies. We used the Balian-Bloch formula [R. Balian and C. Bloch, Ann. Phys. (N.Y.) 84, 559 (1974), and 64, 271 (1971), Eq. (I.1)] for electromagnetic waves in a three-dimensional cavity with smooth walls to check that very few resonances were missed up to 14 GHz. After normalizing them with the local mean eigenmode spacing, we unfolded the resonance spectra and found that the distribution of electromagnetic eigenmodes of the irregular 3D microwave cavities displays a statistical behavior characteristic for classically chaotic quantum systems, viz., the Wigner distribution. We found that this result did not depend on the exact irregular shape of the 3D cavity, suggesting that it is universal.