We investigate time-dependent properties of a single-particle model in which
a random walker moves on a triangle and is subjected to nonlocal boundary
conditions. This model exhibits spontaneous breaking of a Z2 symmetry. The
reduced size of the configuration space (compared to related many-particle
models that also show spontaneous symmetry breaking) allows us to study
the spectrum of the time evolution operator. We break the symmetry explicitly
and find a stable phase, and a metastable phase which vanishes at a spinodal
point.