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We theoretically investigate charged collective modes in a two-dimensionalconductor with hot electrons where the instantaneous mode frequencies graduallyincrease or decrease with time. We show that the loss compensation or evenamplification of the modes may occur. We apply our theory to two types ofcollective modes in graphene, the plasmons and the energy waves, which can beprobed in optical pump-probe experiments.

Adiabatic amplification of plasmons and demons in 2D systems