Dynamics of stripes in doped antiferromagnets

We study the dynamics of the striped phase, which has previously been suggested to be the ground state of a doped antiferromagnet. Starting from the $t-J$ model, we derive the classical equation governing the motion of the charged wall by using a fictitious spin model as an intermediate step. A wavelike equation of motion is obtained and the wall elasticity and mass density constants are derived in terms of the $t$ and $J$ parameters. The wall is then regarded as an elastic string that will be trapped by the pinning potential produced by randomly distributed impurities. We evaluate the pinning potential and estimate the threshold electric field that has to be applied to the system in order to release the walls. Besides, the dynamics of the stripe in the presence of a bias field below the threshold is considered and the high- and low-temperature relaxation rates are derived.