Quantum Boltzmann equation from weakly interacting many-fermion dynamics
In plain words
For weakly interacting quantum particles, collisions are described by a Boltzmann equation with quantum corrections for Pauli blocking, the rule that two fermions cannot share a state. Its derivation from the many-body Schrodinger equation is open.
Precise statement
$N$ fermions in $R^{3}$ with pair interaction $\lambda V$, kinetic scaling $t = T \lambda^{-2}$, $\lambda \to 0$. Prove that the Wigner function of the one-particle density matrix converges to a solution of the Uehling-Uhlenbeck (quantum Boltzmann) equation for $0 < T < T_{0}$. Answer: a proof.
What would settle it
A convergence proof for the full many-body dynamics, not only for a truncated expansion.
Status in the literature
Erdos, Salmhofer and Yau (2004) derived the collision term to second order in a series expansion; the linear Boltzmann equation is proven for one particle in a random potential.