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We study the possibility of spatially non-uniform ground state in(1+1)-dimensional models with quartic fermi interactions at finite fermiondensities by introducing chemical potential \mu. We examine the chiralGross-Neveu model and the Cooper pair model as toy models of the chiralsymmetry breaking and the difermion pair condensates which are presumed toexist in QCD. We confirm in the chiral Gross-Neveu model that the ground statehas a crystalline structure in which the chiral condensate oscillates in spacewith wave number 2\mu. Whereas in the Cooper pair model we find that the vacuumstructure is spatially uniform. Some discussions are given to explain thisdifference.Comment: 18 pages, REVTeX, 3 eps figure

Crystalline ground state in chiral Gross-Neveu and Cooper pair models at finite densities