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In this work we investigate the issue of integrability in a classical modelfor noninteracting fermionic fields. This model is constructed viaclassical-quantum correspondence obtained from the semiclassical treatment ofthe quantum system. Our main finding is that the classical system, contrary tothe quantum system, is not integrablein general. Regarding this contrast it isclear that in general classical models for fermionic quantum systems have to behandled with care. Further numerical investigation of the system showed thatthere may be islands of stability in the phase space. We also investigated asimilar model that is used in theoretical chemistry and found this one to bemost probably integrable, although also here the integrability is not assuredby the quantum-classical correspondence principle.

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