Timeline for Does random phase approximation (RPA) response function obey Kramers-Kronig relations?
Current License: CC BY-SA 3.0
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| May 28, 2017 at 12:06 | comment | added | Alexey Sokolik | Thank you! But I don't understand what do you mean by "resolving second-order pole by first-order poles". For example, if $A_\Pi(\omega)=(a/\pi)/[(\omega-\omega_0)^2+a^2]$ (Lorentzian spectral function), then $\Pi(\omega)=(1/2\pi)(\omega-\omega_0+ia)^{-1}$, i.e. $\Pi(\omega)$ has the first-order pole at $\omega=\omega_0-ia$, which means existence of a damped excitation. At the same time, $\Pi(\omega)=(1/2\pi)^2(\omega-\omega_0+ia)^{-2}$ still has the second-order pole at $\omega=\omega_0-ia$, as can be obtained either by direct squaring of $\Pi(\omega)$ or by using the function $A_\Pi^{(2)}$. | |
| May 26, 2017 at 20:00 | history | edited | Everett You | CC BY-SA 3.0 |
added 449 characters in body
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| May 26, 2017 at 19:50 | history | answered | Everett You | CC BY-SA 3.0 |