Theory on Plasmon Modes of the Cell Membranes

Considering the plasmon oscillation of each layer of the cell membranes as a quasi-particle, we introduce a simple model for the membrane collective charge excitations, take into account the surface effective potential of the plasmon-plasmon interaction between two layers. By using the useful Bogoliubov transformation method, we easily obtained the expressions of the frequencies of plasmon oscillations as a function of wave-number $k$ and membrane thickness $d$, magnitude of these frequencies is in the order of $\sqrt{kd}$. Our results are in good agreement with ones obtained by E. Manousakis.