{"record":{"author":{"account_ref":null,"orcid":null},"builds_on":[],"content_schema":"pubphys.content.revision/1","content_sha256":"23215b64adc2a37c862e296e88236a5a413990cec06e36fc8b8cb14dcc0c2262","created":"2026-10-03T07:18:06Z","files":[],"origin":{"assisted_by":[],"kind":"seed"},"parents":["5475cf5dc5b1a72283d26dc95dc6e00d7ea4e00096a7c6492e409a1816eeb011"],"salt":"34f71c8da8298d6104e306a5c3ae9b92cf8f035d060cc3a050e7e4cf4cf9e6ff","schema":"pubphys.record/2","site":"pubphys.com","target":null,"type":"revision"},"content":{"answer_type":"proof","assisted_by":[],"external_id":"mathph.kinetic-limits.quantum-boltzmann","kind":"well-posed","literature_status":"open","n":"1","parents":[],"plain":"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.","posed_since":"","precise":"$N$ 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.","problem_ref":null,"references":"","settled_by":"A convergence proof for the full many-body dynamics, not only for a truncated expansion.","status_note":"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.","title":"Quantum Boltzmann equation from weakly interacting many-fermion dynamics","topic_ref":"43f072b403d62b3c8ec7e10cd7a52d571053d785f7f84ce0ccb5bff0a60b87cc"},"attested":{"attestation":{"batch":null,"client_id":null,"id_token_sha256":null,"kind":"platform"},"record_hash":"5e5585532db23530359b349657a63176eefd344f59468aa7b59101180bb5f5bf","schema":"pubphys.attested/1"},"envelope":{"attested_hash":"addf412b66cdf57b7711b112bfcf542a00be07caa8d4f103fa043df41b010299","platform_signature":{"key_id":"c6afc19b31429869751f06879c75cd64ea92654423d15b44be775bf1310a60da","sig":"4yNPd5MGZCrfx7ItIUN-zr5incnjxDe2S04GTZJBb3TRmiJ0pDTKq3iB_jtJg22OotoFTVzviA0uDuvdr-JFBA"},"schema":"pubphys.envelope/1"},"record_hash":"5e5585532db23530359b349657a63176eefd344f59468aa7b59101180bb5f5bf","leaf_index":1639}