Raychaudhuri-Ehlers Kinematics on Quantum State-Space: Caustics and Extrinsic Quantum Geometry

arXiv:2611.05499v1 Announce Type: new Abstract: Quantum mechanics is inherently geometric in that the pure states form a curved complex manifold and the Schr\"odinger evolution defines a Hamiltonian flow on this space. Geometry identifies constraints on flows on quantum state-space that hold independently of their microscopic realization. We uncover such universal behavior in families of geodesic paths on the quantum state-space using the Raychaudhuri-Ehlers equations. We show that the complex structure leads to tidal anisotropy in the curvature, and for Hilbert space dimension $N\geq3$, complete point-emitted geodesic bundles necessarily develop shear and undergo direction-selective focusing at finite distance.