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Frequency-dependent shear viscosity of a liquid 2D dusty plasma

The viscoelasticity of a two-dimensional liquid strongly-coupled dusty plasma is studied experimentally, without macroscopic shear. Positions and velocities of the dust particles, measured by video microscopy, are used as the inputs to the generalized Green-Kubo relation to obtain the complex viscosity $η(ω)$. The real part of $η(ω)$ (which corresponds to dissipation) diminishes gradually with frequency, while the imaginary part (which corresponds to elasticity) is peaked at a frequency below the 2D dusty plasma frequency. The viscoelastic approximation is found to accurately describe the 2D experimental results for $η(ω)$, yielding the Maxwell relaxation time $τ_M = 0.10 s$. Results for $η(ω)$ are compared to 2D molecular dynamics Yukawa simulations and to a previous experiment that was performed using an oscillating macroscopic shear.