Spin and Charge Excitations in Incommensurate Spin Density Waves

Dynamical longitudinal spin susceptibility cursive chi_zz (q, ω) and charge density susceptibility cursive chi_nn (q, ω) are evaluated within random phase approximation for incommensurate spin density waves, or stripes, in two dimensional Hubbard model. Taking into account all possible higher harmonics of the fundamental component of the order parameter, we calculate these quantities for the full ranges of the momentum and energy, and analyze collective modes related to the motion of the stripe line. The anisotropy of the dispersion cone comes from the moving pattern of the stripes, i.e., the compression mode or the meandering mode. In the metallic stripe, there are also nesting excitations of the parallel sheet of the Fermi surfaces. We also discuss the excitation of the silent position in the insulating stripe.