Aspects of integrability in a classical model for non-interacting fermionic fields

TL;DR

This paper examines the integrability of a classical model for non-interacting fermionic fields, revealing that unlike its quantum counterpart, the classical system is generally non-integrable, with some stable phase space regions.

Contribution

It demonstrates that classical models derived from quantum fermionic systems are not necessarily integrable, highlighting the need for careful analysis in such classical-quantum correspondences.

Findings

Classical fermionic models are generally non-integrable.

Numerical analysis shows possible islands of stability.

A similar chemistry model is likely integrable but not guaranteed by quantum-classical correspondence.

Abstract

In this work we investigate the issue of integrability in a classical model for noninteracting fermionic fields. This model is constructed via classical-quantum correspondence obtained from the semiclassical treatment of the quantum system. Our main finding is that the classical system, contrary to the quantum system, is not integrablein general. Regarding this contrast it is clear that in general classical models for fermionic quantum systems have to be handled with care. Further numerical investigation of the system showed that there may be islands of stability in the phase space. We also investigated a similar model that is used in theoretical chemistry and found this one to be most probably integrable, although also here the integrability is not assured by the quantum-classical correspondence principle.