In Two Dimensions
In two dimensions the change in conductivity due to either weak localization or weak anti-localization can be described by the Hikami-Larkin-Nagaoka equation:
In this equation is -1 for weak localization and +1/2 for weak anti-localization. is roughly the magnetic field required to disrupt localization effects, and is equal to where is the coherence length. is the digamma function.
Read more about this topic: Weak Localization
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