  We study decoherence of the external degree of freedom of a tracer particle
moving in a one dimensional dilute Boltzmann gas. We find that phase averaging
is the dominant decoherence effect, rather than information exchange between
tracer and gas particles. While a coherent superposition of two wave packets
with different mean positions quickly turns into a mixed state, it is
demonstrated that such superpositions of different momenta are robust to phase
averaging, until the two wave packets acquire a different position due to the
different velocity of each wave packet.
