Bifurcation in kinetic equation for interacting Fermi systems
Nuclear Theory
2016-09-08 v5 Statistical Mechanics
Strongly Correlated Electrons
Chaotic Dynamics
Plasma Physics
Quantum Physics
Abstract
The finite duration of collisions appear as time-nonlocality in the kinetic equation. Analyzing the corresponding quantum kinetic equation for dense interacting Fermi systems a delay differential equation is obtained which combines time derivatives with finite time stepping known from the logistic mapping. The responsible delay time is explicitly calculated and discussed. As a novel feature oscillations in the time evolution of the distribution function itself appear and bifurcations up to chaotic behavior can occur. The temperature and density conditions are presented where such oscillations and bifurcations arise indicating an onset of phase transition.
Cite
@article{arxiv.nucl-th/0012028,
title = {Bifurcation in kinetic equation for interacting Fermi systems},
author = {Klaus Morawetz},
journal= {arXiv preprint arXiv:nucl-th/0012028},
year = {2016}
}