Charge fractionalization beyond the Luttinger liquid paradigm: An analytical consideration

In this paper we consider analytically the density evolution of a spinless Fermi liquid with nonlinear dispersion into which one particle is injected. The liquid interaction is point-like and the temperature is zero. We obtain a formula for the evolution of the density deviation and discuss the picture it gives as well as the physics behind it. We find further fractionalization of the initial density hump comparing to the linear dispersion case: it splits into three humps instead of two. All three change their shapes in a complicated sort of way, and we analyse the mechanisms of these phenomena. We also show that the fractionalization can be illustrated from a semiclassical point of view.