  As a toy model for the microscopic description of matter in de Sitter space,
we consider a Hamiltonian acting on the spin-j representation of SU(2). This is
a model with a finite-dimensional Hilbert space, from which quasinormal modes
emerge in the large-spin limit. The path integral over coherent spin states can
be evaluated at the semiclassical level and from it we find the single-particle
de Sitter density of states, including 1/j corrections. Along the way, we
discuss the use of quasinormal modes in quantum mechanics, starting from the
paradigmatic upside-down harmonic oscillator.
