Weak chaos in the string $S$-matrix

We consider the scattering of tachyons, photons and gravitons off highly excited strings and study the signs of chaos in the resulting $S$-matrix. We find that the $S$-matrix (unlike individual amplitudes) never exhibits clear chaotic behavior, i.e. it never satisfies the eigenphase repulsion statistics expected in a chaotic scattering problem. Instead, the eigenphase spectrum has both regular and chaotic contributions, and the regular component persists even when the total occupation number of the string grows to infinity. We further consider the influence of ensemble averaging over the excited string states and also try to approach the string/black hole transition point. The conclusion is that the onset of fast scrambling cannot be seen from the string $S$-matrix, even though we can see some other signs of the string/black hole transition.