Hysteretic behaviour of a simple Charge Density Wave system

In this thesis, the hysteretic behaviour in a simple 1D Charge Density Wave (CDW) system is investigeted. Such systems can be represented as elastically coupled particles in a periodic potential with a random phase-offset in the presence of a uniform external force. CDWs are models for depinning transitions: for a force smaller then a threshold force, all configurations are static, while a sliding dynamic behavior is obtained when the threshold force is exceeded. The systems we consider have two unique and distinct threshold configurations, corresponding to reaching the threshold via positive and negative force increments. We study how hysteresis occurs in between these two threshold configurations. For a fixed system size, there are finite number of pinned states that can be obtained by arbitrarily varying the external force while keeping the system in the pinned onfiguration.We find a power law relation between system size L and the total number of reachable states which are the configurations that can be reached from the threshold configurations by equence of increasing or decreasing forces. We also observe that our model has the return-point memory effect.