Laser Physics

On fully quantum kinetic equations for BEC, new theorem on nonpolynomial averages, and new special numbers enumerating one-cycle oriented graphs

Vitaly V. Kocharovsky, Vl. V. Kocharovsky

Published May 1, 2007• 11 citations

Abstract

We find the analytical formulas for a full nonlinear rate of condensation and for a collision integral in fully quantum kinetic equations for a homogeneous Bose-Einstein condensation which go beyond the previously known semiclassical kinetic equations where only a linear stimulated rate was taken into account. These formulas yield, in particular, a rate of spontaneous condensation and allow us to address a long-standing problem on the mechanism of a BEC phase transition governed by the nonperturbation effects of quantum fluctuations in a many-body system. The results are obtained with the help of a new general theorem on nonpolynomial averages in statistical physics that amounts to an exact summation of a full infinite set of Wick’s diagrams. We present in some details a derivation of these nonperturbation-in-fluctuations results as well as the general theorem based on the newly introduced special numbers enumerating one-cycle oriented graphs.

DOI: 10.1134/s1054660x07050167

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