Analyzing symmetry breaking within a chaotic quantum system via Bayesian inference.pdfVIP

Analyzing symmetry breaking within a chaotic quantum system via Bayesian inference C. I. Barbosa and H. L. Harney Max-Planck-Institut f¨ur Kernphysik, D-69029 Heidelberg, Germany (February 2, 2008) Bayesian inference is applied to the level fluctuations of two coupled microwave billiards in order to extract the coupling strength. The coupled resonators provide a model of a chaotic quantum 9 system containing two coupled symmetry classes of levels. The number variance is used to quantify 9 the level fluctuations as a function of the coupling and to construct the conditional probability 9 distribution of the data. The prior distribution of the coupling parameter is obtained from an 1 invariance argument on the entropy of the posterior distribution. t c PACS number(s): 02.50.Wp, 05.45.+b, 11.30.Er O 5 I. INTRODUCTION eigenvalues of random matrices drawn from the GOE. In 2 order to assess these fluctuations, various statistics have ] The subject of the present paper is Bayesian inference been defined — such as the distance of neighboring levels n as applied to the experiment of Ref. [1] in order to extract or the variance of the number of levels in a given inter- a val. The expectation values of these statistics have been - the mean square matrix element coupling two chaotic a classes of quantum states. The Baye