Weak localization Bergmanns treatment

The constant C is uncertain, but we give evidence that it is unity. However, if some collisions are inelastic, this interference does not take place. We therefore introduce the inelastic diffusion length 

The inelastic collisions can be either with another electron, when TjOcT-2 (cf. Section 10) or with phonons, when above the Debye temperature TjOcT-1. 

These effects are described as weak localization . Experimental evidence for the effects predicted for amorphous metals is described in Chapter 10. It will be seen that the effects are only significant when l is small, and thus typically for noncrystalline materials. It is remarkable that, as a consequence of (51), inelastic scattering increases the conductivity. 

An equation of the type (51) has been obtained independently by other authors. The earliest (Kawabata 1981) is used in the next section. Fritsch et al (1987), on the basis of the work of the Munich school, give 

Morgan et al (1985) have developed an expression for the correcting term that is claimed to go beyond perturbation theory, and to be exact. However, it does not agree in the weak-perturbation limit with the formulae described above, giving a correction in (kl) 2F1/2, where F diverges logarithmically when (kiy O. 

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