An an exactly solvable quantum model is found to sample the evolution towards
the sudden and complete loss of observability. For the purpose we choose an
N-level system. While the time runs from 0 to 1, the process (leading to the
collapse) is controlled by a toy-model Hamiltonian H and by a unitary-evolution
guaranteeing minimally anisotropic (i.e., unique) Hilbert-space metric. The
process of the degeneracy of the real N-plet of energy levels is studied
without the usual assumption of adiabaticity. The initial Hamiltonian is
diagonal, the initial metric is chosen as identity. Once the system reaches the
observability horizon, the metric becomes singular (of rank one) while the
end-point Hamiltonian acquires the canonical Jordan-block form (i.e., it loses
its diagonalizability). An optimal measure of the distance from the final
catastrophe is finally found in a universal, exact formula for the spectrum of
the metric.Comment: 19 pp., 4 figures, 4 table
