  Pair collisions in atomic gases lead to decoherence and decay. Assuming that
all the atoms in the gas are equally likely to collide one is led to consider
Lindbladian of mean field type where the evolution in the limit of many atoms
reduces to a single qudit Lindbladian with quadratic non-linearity. We describe
three smoking guns for non-linear evolutions: Power law decay and dephasing
rates; Dephasing rates that take a continuous range of values depending on the
initial data and finally, anomalous flow of the Bloch ball towards a
hemisphere.
