The paper deals with the numerical study of the electromagnetic response of a metallic nanoparticle to an external field, within the framework of the classical electrodynamics. The conduction electrons of the nanoparticle are modeled as a compressible electron gas, whose dynamics are described by means of the linearized hydrodynamic equations. The fluid pressure arising from the kinetic energy of the degenerate electron gas gives arise to non-local effects, which may influence strongly the plasmon resonances.
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