Not to normal order - Notes on the kinetic limit for weakly interacting quantum fluids

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dc.creatorLukkarinen, Jani
dc.creatorSpohn, Herbert
dc.date2008-07-31
dc.date2008-11-11
dc.date.accessioned2026-07-07T13:17:22Z
dc.date.available2026-07-07T13:17:22Z
dc.descriptionThe derivation of the Nordheim-Boltzmann transport equation for weakly interacting quantum fluids is a longstanding problem in mathematical physics. Inspired by the method developed to handle classical dilute gases, a conventional approach is the use of the BBGKY hierarchy for the time-dependent reduced density matrices. In contrast, our contribution is motivated by the kinetic theory of the weakly nonlinear Schrodinger equation. The main observation is that the results obtained in the latter context carry over directly to weakly interacting quantum fluids provided one does not insist on normal order in the Duhamel expansion. We discuss the term by term convergence of the expansion and the equilibrium time correlation <a(t)* a(0)>.
dc.description43 pages, corrected typos, updated assumptions in sec. 7
dc.identifierhttps://arxiv.org/abs/0807.5072
dc.identifierhttp://arxiv.org/abs/0807.5072
dc.identifierJ. Stat. Phys. 134 (2009) 1133-1172
dc.identifierdoi:10.1007/s10955-009-9682-8
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/231094
dc.subjectMathematical Physics
dc.subjectQuantum Physics
dc.subject82C10; 82C40
dc.titleNot to normal order - Notes on the kinetic limit for weakly interacting quantum fluids
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