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Journal of Statistical Physics

, Volume 59, Issue 3–4, pp 725–744 | Cite as

On the Snider equation

  • F. Laloë
  • W. J. Mullin
Articles

Abstract

We study the physical content of the Snider quantum transport equation and the origin of a puzzling feature of this equation, which implies contradictory values for the one-particle density operator. We discuss in detail why the two values are in fact not very different provided that the studied particles have sufficiently large wave packets and only a small interaction probability, a condition which puts a limit on the validity of the Snider equation. In order to improve its range of application, we propose a reinterpretation of the equation as a “mixed” equation relating the real one-particle distribution function (on the left-hand side of the equation) to the “free” distribution (on the right-hand side), which we have introduced in a recent contribution. In its original form, the Snider equation is valid only when used to generate Boltzmann-type equations where collisions are treated as point processes in space and time (no range, no duration); in this approximation, virial corrections are not included, so that the real and free distributions coincide. If the equation is used beyond this approximation to generate nonlocal and density corrections, we conclude that the results are not necessarily correct.

Key words

Boltzmann equation transport equation Snider equation BBGKY hierarchy virial corrections molecular fields 

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Copyright information

© Plenum Publishing Corporation 1990

Authors and Affiliations

  • F. Laloë
    • 1
  • W. J. Mullin
    • 2
  1. 1.Département de Physique de l'ENSParisFrance
  2. 2.Department of PhysicsUniversity of MassachusettsAmherst

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