VORTEX INTERACTIONS IN THE COMPLEX GINZBURG-LANDAU EQUATION

Extended non-equilibrium systems exhibit a variety of phenomena that have similar counterparts in equilibrium systems. Examples include super and subcritical instabilities, the counterparts of which are second and first order phase transitions, defect dynamics in convective patterns which have much in common with the analogous dynamics in crystals [1], and defect mediated turbulence which is reminiscent of two-dimensional melting [2]. The analogy between equilibrium and non-equilibrium phenomena, however, do not go too far. One distinctive feature whose consequences have been studied recently in a number of contexts [3,4] is the non-variational nature of the equations which govern non-equilibrium systems. The absence of a free-energy or a Liapunov functional makes the study of these equations more difficult and calls for different analytical tools. In this paper we study vortex dynamics in non-equilbrium two-dimensional systems; we show how vortex interactions can be derived in the absence of a free-energy functional, and discuss new qualitative features that arise in this case.