  The eigenstate decoherence hypothesis (EDH) asserts that each individual
eigenstate of a large closed system is locally classical-like. We test this
hypothesis for a heavy particle interacting with a gas of light particles. This
system is paradigmatic for studies of the quantum-to-classical transition: The
reduced state of the heavy particle is widely believed to rapidly loose any
nonclassical features due to the interaction with the gas. Yet, we find
numerical evidence that the EDH is violated: certain eigenstates of this model
are manifestly non-classical. Only the weak version of EDH referring to the
majority (instead of the totality) of eigenstates holds.
