FLUCTUATION-INDUCED INTERACTIONS BETWEEN RODS ON A MEMBRANE

We consider the interaction between two rods embedded in a fluctuating surface. The modification of fluctuations by the rods leads to an att ractive long-range interaction between them. We consider fluctuations governed by either surface tension (films) or bending rigidity (membra nes). In both cases the interaction falls off with the separation of t he rods as 1/R(4). The orientational part of the interaction is propor tional to cos(2)[theta(1)+theta(2)] in the former case and to cos(2)[2 (theta(1)+theta(2))] in the latter, where theta(1) and theta(2) are an gles between the rods and the line joining them. These interactions ar e somewhat reminiscent of dipolar forces and will tend to align collec tions of such rods into chains.