ON THE SNIDER EQUATION

Publication Date

1990

Journal or Book Title

JOURNAL OF STATISTICAL PHYSICS

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 ldquomixedrdquo equation relating the real one-particle distribution function (on the left-hand side of the equation) to the ldquofreerdquo 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.

Comments

Published version is located at http://www.springerlink.com/content/v27251756h177251/

Pages

725-744

Volume

59

Issue

3-4

Link to Full Text

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