Abstract
This paper investigates the fluctuation-induced interaction between flexible ideal polymer chains on membranes. Tiny fluctuations happen in the vicinity of the curved surface of the membrane where the potential energy is in the lowest value. The fluctuations are governed by the Helfrich effective surface energy and the effective interaction energy. Under this viewpoint, the energy and the entropy corresponds to one-point and two-point Green function, respectively. The variations of surface energy and the leading-term interaction between chains are calculated with chains anchored to a membrane and strongly confined between two planar membranes in the three dimensional space.
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