Experimental study of quantum chaos with acoustic resonators

Author(s)

Thiago Nascimento Nogueira

• Document type: Doctoral Thesis
• Press: São Paulo.
• Institution: Universidade de São Paulo (USP). Instituto de Física (IF/SBI)
• Defense date: 2006-12-14

Examining board members

Jose Carlos Sartorelli; Paulo Batista Gonçalves; Maria Carolina Nemes; Alfredo Gontijo de Oliveira; Antonio Domingues dos Santos

• Advisor: Jose Carlos Sartorelli

Abstract

We have built an experimental apparatus to study acoustic resonators which have been considered as classical analogs of quantum billiards. The equipment was able to keep the stability during several days, which is a requirement to the precise eigenfrequency measurements allowing a characterization of the systems. We have characterized 7 samples made of aluminum plates with thickness smaller than 2 mm having the following geometries: two Sinai\'s stadiums (with and without planar symmetry), an equilateral triangle, a rectangle triangle, and a scalene triangle with three acute and irrational angles, and two circular shaped samples, with and without planar symmetry. We observed that three of the samples followed the GOE statistics (the asymmetrical Sinai stadium, the rectangle triangle and the scalene one). The asymmetrical Sinai stadium was described by 2GOE statistics, the equilateral triangle by the semi-Poisson, the symmetrical circle by a Poisson with missing levels and the asymmetrical circle has statistics apparently between 1GOE and 2GOE which was not possible to classify. The high quality of data allowed us to calculate the spectra energies and we found these results compatible with the previous one. (AU)