Statistics of eigenfunctions of chaotic billiards taking account of the Rashba spin-orbit interaction

It is demonstrated, both analytically and numerically, that eigenfunction statistics in chaotic billiards with spin-orbit interaction fundamentally depend on the ratio of the squared spin-orbit interaction constant. If this ratio is small, one of the eigenstate components is a random Gaussian field, whereas another is not universal and depends on the billiard type. In the opposite case, the statistics of both components is described by the independent random complex Gaussian fields with the same variances. In the intermediate case, both eigenfunction components do not satisfy Gaussian statistics.