We study the N_f-flavor Gross-Neveu model in 2+1 dimensions with a baryon
chemical potential mu, using both analytical and numerical methods. In
particular, we study the self-consistent Boltzmann equation in the Fermi liquid
framework using the quasiparticle interaction calculated to O(1/N_f), and find
solutions for zero sound propagation for almost all mu > mu_c, the critical
chemical potential for chiral symmetry restoration. Next we present results of
a numerical lattice simulation, examining temporal correlation functions of
mesons defined using a point-split interpolating operator, and finding evidence
for phonon-like behaviour characterised by a linear dispersion relation in the
long wavelength limit. We argue that our results provide the first evidence for
a collective excitation in a lattice simulation.Comment: 18 pages, 6 figure