  We question the microcanonical hypothesis, often made to account for the
thermalization of complex closed quantum systems, on the specific example of a
chain of two-level atoms optically driven by a resonant laser beam and strongly
interacting via Rydberg-Rydberg dipole-dipole interactions. Along its
(necessarily unitary) evolution, this system is indeed expected to thermalize,
i.e. observables, such as the number of excitations, stop oscillating and reach
equilibrium-like expectation values. The latter are often calculated through
assuming the system can be effectively described by a thermal-like
microcanonical state. Here, we compare the distribution of excitations in the
chain calculated either according to the microcanonical assumption or through
direct exact numerical simulation. This allows us to show the limitations of
the thermal equilibrium hypothesis and precise its applicability conditions.
