Testing eigenstate decoherence hypothesis in a model of collisional decoherence

An eigenstate decoherence hypothesis (EDH) states that each individual eigenstate of a large closed system is locally classical-like. We test this hypothesis for a system paradigmatic for the studies of quantum-to-classical transition: A heavy particle immersed in a gas. The coherence lengths of the heavy particle in many-body eigenstates are calculated. We address an integrable case of an infinitely heavy particle and a nonintegrable case of a particle of a finite mass. For the latter case we obtain a numerical evidence that the EDH is valid in the strong sense, i.e. for any eigenstate. In the former case the strong EDH is demonstrated in the case of nondegenerate many-body spectrum. However, if the model is integrable and the spectrum is degenerate (due to a symmetry of the Hamiltonian), the strong EDH is violated – there are eigenstates with the coherence length diverging in the thermodynamic limit. This remarkable result is at odds with the predictions of the theory of collisional decoherence and thus reveals its limitations. The remnant of this effect can be seen in the nonintegrable model, where we find eigenstates with anomalously large (though apparently finite in the thermodynamic limit) coherence lengths.