GLOBALLY COUPLED DYNAMICS OF BREATHING CURRENT FILAMENTS IN SEMICONDUCTORS

Starting from a system of nonlinear transport equations describing the dynamics of a single breathing current filament, e.g. in the regime of low-temperature impurity breakdown in semiconductors, we introduce a simple nonlocal coupling mechanism for the description of two breathing filaments. It is based on the interaction of the two filaments via the external load circuit. We find that the model describes a selection mechanism allowing the survival of the originally larger filament only. Therefore, it can be considered a generalization of Ostwald ripening in thermodynamic equilibrium. Although the breathing instability is suppressed asymptotically, transient symmetric breathing of the filaments is possible due to a periodic repeller.