Study of the collision operator, ψ(z), for some exactly soluble models
Abstract
The collision operator, ψ( z), introduced in the study of nonequilibrium statistical mechanics by Prigogine, Balescu, and Résibois is calculated exactly for some simple quantummechanical models. The calculations are done first for the discreteenergy spectrum case. Then, the behavior of the solutions is studies in the limit: l (extension of the system) → ∞, where continua appear in the spectra. It is found that the exact collision operators ψ( z, l) posses the property that lim _{z}_{→0} ψ ( z, l) is either zero or underfined for finite l, while lim_{z}_{→10+}lim_{l}_{→∞}ψ ( z, l) is a nonzero operator.
 Publication:

Physica
 Pub Date:
 November 1972
 DOI:
 10.1016/00318914(72)901322
 Bibcode:
 1972Phy....62..301G