Localized and unlocalized structures in nonlinear lattices with fermions

Full text: We study the quasiclassical approximation for the equations of motion of a nonlinear chain of phonons and electrons having phonon mediated hopping. Describing the phonons and electrons as even and odd grassmanian functions and using the continuum limit we show that the equations of motion lead to a Zakharov-like system for bosonic and fermionic fields. Localized and nonlocalized solutions are discussed using Hirota bilinear formalism. Nonlocalized solutions turn out to appear naturally for any choice of wave parameters. The bosonic localized solution has a fermionic dressing while the fermionic one is the oscillatory localized field. They appear only if some constraints on the dispersion are imposed. In this case the density of fermions is a strongly localized traveling wave. Also it is shown that in the multiple scales approach the emergent equation is linear. Only for the resonant case we get a nonlinear fermionic Yajima-Oikawa system. Physical implications are discussed. (author)