Non-Linear Waves in Fermi Liquids

Abstract

I show that when non-linearities are taken into account the Landau theory of Fermi liquids predicts the existence of hyperbolic waves in fermionic systems. The zero sound is described by a infinite set of coupled non-linear partial differential equations, one for each harmonic of oscillation of the Fermi surface. When just a few harmonics are included it is possible to describe the dynamics of the first sound in a very simple way. These results lead to the interesting experimental possibility of having non-linear effects in quantum liquids. In particular I discuss the problem of generation of second harmonic in a Fermi system.