  We study the possibility of spatially non-uniform ground state in
(1+1)-dimensional models with quartic fermi interactions at finite fermion
densities by introducing chemical potential \mu. We examine the chiral
Gross-Neveu model and the Cooper pair model as toy models of the chiral
symmetry breaking and the difermion pair condensates which are presumed to
exist in QCD. We confirm in the chiral Gross-Neveu model that the ground state
has a crystalline structure in which the chiral condensate oscillates in space
with wave number 2\mu. Whereas in the Cooper pair model we find that the vacuum
structure is spatially uniform. Some discussions are given to explain this
difference.
