  We develop an innovative technique for studying inhomogeneous phases with a
spontaneous broken symmetry. The method relies on the knowledge of the exact
form of the free energy in the homogeneous phase and on a specific gradient
expansion of the order parameter. We apply this method to quark matter at
vanishing temperature and large chemical potential, which is expected to be
relevant for astrophysical considerations. The method is remarkably reliable
and fast as compared to performing the full numerical diagonalization of the
quark Hamiltonian in momentum space, and is designed to improve the standard
Ginzburg-Landau expansion close to the phase transition points. For
definiteness we focus on inhomogeneous chiral symmetry breaking, accurately
reproducing known results for 1D and 2D modulations and examining novel
crystalline structures, as well. Consistently with previous results, we find
that the energetically favored modulation is the so-called 1D real kink
crystal. We propose a qualitative description of the pairing mechanism to
motivate this result.
