Theory on Plasmon Modes of the Cell Membranes

TL;DR

This paper develops a theoretical model for plasmon modes in cell membranes, describing their collective charge oscillations and deriving frequency expressions that align with previous findings.

Contribution

It introduces a simple quasi-particle model for membrane plasmons considering interlayer interactions and uses Bogoliubov transformation to derive frequency formulas.

Findings

Derived plasmon frequency expressions as a function of wave-number and membrane thickness.

Frequency magnitudes are proportional to the square root of wave-number times thickness.

Results agree with previous theoretical work by E. Manousakis.

Abstract

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.