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Here is a sketch of a derivation of the Kubo formula: Write the full Hamiltonian $H=H_0+H'e^{-\eta t}$ where $H'$ is an external (time-independent) perturbation and $\eta\rightarrow 0$. We would like to evaluate the expectation value of an operator $A(t)$: $\langle A(t)\rangle=\mathrm{Tr}[\rho(t)A(t)]$. So we need to first determine $\rho(t)$ using ...

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