In this contribution I describe the problem of deriving a Boltzmann equation for a system of N interacting quantum particles under the weak‐coupling and the low density limits, showing that the limiting behavior of the one‐particle Wigner function is expected to satisfy a Boltzmann equation with a suitable cross‐section.
The problem is still open from a rigorous view point and only partial results are available till now. The talk is based on a sistematic collaboration with D. Benedetto, F. Castella and R. Esposito.
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