Testing eigenstate decoherence hypothesis in a model of collisional decoherence

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 non-classical 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.