Describing and understanding the essence of quantum entanglement and its
connection to dynamical chaos is of great scientific interest. In this work,
using information geometric (IG) techniques, we investigate the effects of
micro-correlations on the evolution of maximal probability paths on statistical
manifolds induced by systems whose microscopic degrees of freedom are Gaussian
distributed. We use the statistical manifolds associated with correlated and
non-correlated Gaussians to model the scattering induced quantum entanglement
of two spinless, structureless, non-relativistic particles, the latter
represented by minimum uncertainty Gaussian wave-packets. Knowing that the
degree of entanglement is quantified by the purity P of the system, we express
the purity for s-wave scattering in terms of the micro-correlation coefficient
r - a quantity that parameterizes the correlated microscopic degrees of freedom
of the system; thus establishing a connection between entanglement and
micro-correlations. Moreover, the correlation coefficient r is readily
expressed in terms of physical quantities involved in the scattering, the
precise form of which is obtained via our IG approach. It is found that the
entanglement duration can be controlled by the initial momentum p_{o}, momentum
spread {\sigma}_{o} and r. Furthermore, we obtain exact expressions for the IG
analogue of standard indicators of chaos such as the sectional curvatures,
Jacobi field intensities and the Lyapunov exponents. We then present an
analytical estimate of the information geometric entropy (IGE); a suitable
measure that quantifies the complexity of geodesic paths on curved manifolds.
Finally, we present concluding remarks addressing the usefulness of an IG
characterization of both entanglement and complexity in quantum physics.Comment: 37 pages, 3 figure
