INCLUSIONS IN FLUCTUATING MEMBRANES - EXACT RESULTS

Point-like inclusions in fluid, fluctuating membranes are considered. Here the term inclusion is used in a general sense and describes a num ber of seemingly disparate situations: particles in membranes or other external and localized forces (such as a laser tweezer) which i) make the membrane locally stiffer, ii) induce a local spontaneous curvatur e, iii) change the local membrane thickness, or iv) the local separati on between neighboring membranes. All these situations can be describe d by linear or quadratic local perturbations, for which the partition function is calculated exactly using a Gaussian membrane model. The de formed shape of a membrane in response to the presence of one inclusio n and the membrane-mediated interactions between inclusions are thus o btained without further approximations. The interaction between two in clusions described by linear perturbations is temperature independent and therefore not affected by membrane fluctuations. The interaction b etween two inclusions described by quadratic perturbations is solely d ue to membrane shape fluctuations and vanishes at zero temperatures; i n the strong coupling limit it shows a universal logarithmic divergenc e at short length scales. Formulas for the interaction of n inclusions are derived, which show non-trivial multibody contributions for the c ase of quadratic inclusions. All these results are valid for all tempe ratures and for all coupling strengths and thus bridge previously obta ined results obtained at zero temperatures (neglecting membrane shape fluctuations) or using perturbation theory (for small strengths of the coupling between the inclusions and the membrane). These exact result s are obtained with general Gaussian Hamiltonians and are thus applica ble to all systems described by Gaussians forms.