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Matalien l\"amp\"otilojen fysiikan teoria (Kyl-0.104)\hfil Autumn 2000\break
Electronic transport in mesoscopic systems\hfil Exercise set 9\break
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1. Exercise E.5.1 from Datta's book. Go also through the simple-minded derivation
of the weak-localization correction to the conductivity in 2 dimensions (pages
207-208):
$$\sigma=\sigma_{\rm cl}-{e^2\over \pi h}\ln{\tau_\phi\over\tau_m}.$$
Use a similar argument to derive in 3 dimensions the following result
$$\sigma=\sigma_{\rm cl}-{e^2\over 2\pi h}({1\over L_m}-{1\over L_\phi}),$$
which probably is correct at least qualitatively. (There is an additional correction
arising from electron-electron interactions, which will not be considered here.) 
Express the relative magnitudes of the weak localization corrections [$(\sigma_{\rm
cl}-\sigma)/\sigma_{\rm cl}$] as a function of $k_FL_m$ in both 2 and 3 dimensions,
and compare their order of magnitude.
\bigskip 

                                                                    
Exercises E.5.2 and E.5.3 from Datta's book. 
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