  Metastable states in stochastic systems are often characterized by the
presence of small eigenvalues in the generator of the stochastic dynamics. We
here show that metastability in many-body systems is not necessarily associated
with small eigenvalues. Instead, many-body explosion of eigenmode expansion
coefficients characterizes slow relaxation, which is demonstrated for two
models, interacting particles in a double-well potential and the
Fredrickson-Andersen model, the latter of which is a prototypical example of
kinetically constrained models studied in glass and jamming transitions. Our
results provide new insights into slow relaxation and metastability in
many-body stochastic systems.
