# How to get conductivity from Green function $\mathcal{G}(x_1,x_2,\tau)$ of inhomogeneous system?

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I'd like to study an inhomogeneous system, i.e., momentum is not a good quantum number therein. Therefore, I tried to calculate temperature Green functions like $\mathcal{G}(x_1,x_2;\tau)$, or its twofold Fourier transformation $\mathcal{G}(p_1,p_2;\tau)$.

But how can I get any transport property, e.g., conductivity, from these Green functions? I checked Mahan's overwhelming book, however, it only deals with the formalism of $\mathcal{G}(p;\tau)$ for homogeneous systems. Thanks in advance for any useful information.

This post imported from StackExchange Physics at 2014-08-22 05:08 (UCT), posted by SE-user huotuichang
asked Feb 21, 2014
If your system is inhomogeneous or has messy boundaries, then the conductivity is probably not given by just one number but rather would be anisotropic.

This post imported from StackExchange Physics at 2014-08-22 05:08 (UCT), posted by SE-user Nanite

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