The chaotic behavior of the Bianchi IX model under the influence of quantum effects

A quantum analysis of the Bianchi IX model in vacuum is performed, focusing on the chaotic nature of the system. Applying some minimal approximations, but constructing a sufficiently general framework, we encode all the information of the quantum degrees of freedom in the fluctuations of the anisotropy parameters. These fluctuations are then described as canonical variables, in order to extend the classical phase space and apply the usual methods of dynamical systems for studying chaos. In particular, two of these techniques are considered. On the one hand, an analytical study is carried out which provides an isomorphism between the quantum dynamics of Bianchi IX and the geodesic flow on a Riemannian manifold, thus extending the usual billiard picture. On the other hand, by means of numerical simulations, the fractal dimension of the boundary between points with different outcomes in the space of initial data is studied. The main conclusion is that, although the quantum system is chaotic, the quantum effects considerably reduce this behavior in comparison with its classical counterpart.