The longitudinal dielectric function of a gas of free electrons (+ homogeneous positive background) is often described in the Lindhard- or Random Phase Approximation (RPA).(adsbygoogle = window.adsbygoogle || []).push({});

The dielectric function depends on both frequency omega and wavevector k. However, it is non-analytic at the point omega=0, k=0. Namely its value depends on how the constant ratio of omega/k is chosen in the limit omega to 0. What is the physics behind this behaviour?

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# Lindhard RPA Dielectric Function Electron Gas

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