Chaos in the Color Glass Condensate

The number of gluons in the hadron wave function is discrete, and their formation in the chain of small $x$ evolution occurs over discrete rapidity intervals of $\Delta y \simeq 1/\as$. We therefore consider the evolution as a discrete quantum process. We show that the discrete version of the mean-field Kovchegov evolution equation gives rise to strong fluctuations in the scattering amplitude, not present in the continuous equation. We find that if the linear evolution is as fast as predicted by the perturbative BFKL dynamics, the scattering amplitude at high energies exhibits a chaotic behavior. As a consequence, the properties of diffraction at high energies become universal.