We derive a model to describe decoherence of atomic clouds in atom-chip traps taking the excited states of the trapping potential into account. We use this model to investigate decoherence for a single trapping well and for a pair of trapping wells that form the two arms of an atom interferometer. Including the discrete spectrum of the trapping potential gives rise to a decoherence mechanism with a decoherence rate $\Gamma$ that scales like $\Gamma \sim 1/r_0^4$ with the distance $r_0$ from the trap minimum to the wire.
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