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We study the charge response in complex frequency plane and the quasi-normalmodes (QNMs) of the boundary quantum field theory with momentum dissipationdual to a probe generalized Maxwell system with Weyl correction. When thestrength of the momentum dissipation $\hat{\alpha}$ is small, the polestructure of the conductivity is similar to the case without the momentumdissipation. The qualitative correspondence between the poles of the real partof the conductivity of the original theory and the ones of its electromagnetic(EM) dual theory approximately holds when $\gamma\rightarrow -\gamma$ with$\gamma$ being the Weyl coupling parameter. While the strong momentumdissipation alters the pole structure such that most of the poles locate at thepurely imaginary axis. At this moment, the correspondence between the poles ofthe original theory and its EM dual one is violated when $\gamma\rightarrow-\gamma$. In addition, for the dominant pole, the EM duality almost holds when$\gamma\rightarrow -\gamma$ for all $\hat{\alpha}$ except for a small region of$\hat{\alpha}$.

Quasi-normal modes of holographic system with Weyl correction and momentum dissipation