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

Jani Lukkarinen, Herbert Spohn

Research output: Contribution to journalArticlepeer-review

35 Scopus citations

Abstract

The 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).

Original languageEnglish
Pages (from-to)1133-1172
Number of pages40
JournalJournal of Statistical Physics
Volume134
Issue number5-6
DOIs
StatePublished - Mar 2009

Keywords

  • Boltzmann-nordheim equation
  • Kinetic theory
  • Quantum bbgky hierarchy
  • Time-dependent perturbation theory
  • Uehling-uhlenbeck equation
  • Weakly interacting bosons
  • Weakly interacting fermions

Fingerprint

Dive into the research topics of 'Not to normal order-notes on the kinetic limit for weakly interacting quantum fluids'. Together they form a unique fingerprint.

Cite this