Modeling of dynamics of field-induced transformations in charge density waves

We present a modeling of stationary states and their transient dynamic for charge density waves in restricted geometries of realistic junctions under the applied voltage or the passing current. The model takes into account multiple fields in mutual nonlinear interactions: the amplitude and the phase of the charge density wave complex order parameter, distributions of the electric field, the density and the current of normal carriers. The results show that stationary states with dislocations are formed after an initial turbulent multi-vortex process. Static dislocations multiply stepwise when the voltage across or the current through the junction exceed a threshold. The dislocation core forms a charge dipole which concentrates a steep drop of the voltage, thus working as a self-tuned microscopic tunnelling junction. That can gives rise to features observed in experiments on the inter-layer tunneling in mesa-junctions