Non-Crossing Effect on Long Wavelength Fluctuation of Multilayer Membrane System

We investigate the fluctuation properties of a multilayer membrane system by means of a capillary-wave (CW) picture. We examine the non-crossing effect between membranes. From the CW picture, we derive a novel Hamiltonian expressing the fluctuation properties, which is different from the Hamiltonian proposed by Helfrich [W. Helfrich: Z. Naturforsch 33a (1978) 305]. To verify the new Hamiltonian, we performed a Monte Carlo simulation on the basis of the Gaussian solid-on-solid model for a one-dimensional multilayer membrane system. The result strongly supports the novel Hamiltonian.