Localised and nonlocalised structures in nonlinear latticeswith fermions

Abstract

We discuss the quasiclassical approximation for the equations ofmotions of a nonlinear chain of phonons and electrons havingphonon-mediated hopping. Describing the phonons and electrons aseven and odd Grassmannian functions and using the continuum limit,we show that the equations of motion, lead to a Zakharov-likesystem for bosonic and fermionic fields. Localised andnonlocalised solutions are discussed using the Hirota bilinearformalism. Nonlocalised solutions turn out to appear naturallyfor any choice of wave parameters. The bosonic localised solutionhas a fermionic dressing while the fermionic one is anoscillatory localised field. They appear only if some constraintson the dispersion are imposed. In this case the density offermions is a strongly localised travelling wave. Also it isshown that in the multiple-scales approach the emergent equationis linear. Only for the resonant case we get a nonlinearfermionic Yajima-Oikawa system. Physical implications arediscussed.