Effect of symmetry breaking on level curvature distributions

We derive an exact general formalism that expresses the eigenvector and the eigenvalue dynamics as a set of coupled equations of motion in terms of the matrix elements dynamics. Combined with an appropriate model Hamiltonian, these equations are used to investigate the effect of the presence of a discrete symmetry in the level curvature distribution. An explanation of the unexpected behavior of the data regarding frequencies of acoustic vibrations of quartz block is provided.