Adiabatic elimination for classical fermionic systems

Abstract

Presents the reduction to a normal form of a Grassmannian differential equation describing a classical fermionic system in the neighbourhood of an instability. As an application of the method presented the author shows that the anticommuting version of the normal form associated with (a) the Hopf bifurcation (a simple pair of imaginary eigenvalues) leads to the overdamped Grassmann harmonic oscillator, and (b) the resonant Hopf bifurcation 1: 1 (a double pair of semisimple imaginary eigenvalues) corresponds exactly to the Thirring model for Grassmann solitons.