For surface plasmons on graphene in an arbitrary dielectric environment, combinations of the plasmon energy and frequency (adiabatic invariants) that are conserved during slow time-variations of the graphene free carrier density are obtained. The invariants allow one to find the plasmon energy changes directly from the frequency shift without solving a dynamic equation. The invariants have a different form in the cases of increasing and decreasing carrier density. In both cases, however, they predict that plasmon frequency shifting is accompanied by a decrease of the plasmon energy.

中文翻译：

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时态动态石墨烯表面等离子体的绝热不变量

对于任意介电环境中石墨烯上的表面等离激元，可以获得在石墨烯自由载流子密度的缓慢时变过程中守恒的等离激元能量和频率的组合（绝热不变量）。不变量使人们可以直接从频移中找到等离子体激元能量的变化，而无需求解动力学方程。在增加和减少载流子密度的情况下，不变量具有不同的形式。但是，在这两种情况下，他们都预测等离子体激元的频移会伴随等离子体激元能量的降低。