Abstract
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(a)
Localization as an unrecognizable monster: e.g., “singular continuous” spectra in almost periodic potentials (Science Magazine, August 14, 1984: “Singular continuous spectra have no physical applications”). ~ 10 years of real history—1974 begins “era of belief”. (Note: 1975, Göttingen Acad. Sci., first recognition.)
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(b)
Localization as a paradigm: Study of dirt effects, e.g., tunneling centers, aggregation, percolation, Kohlrausch relaxation in glass.
Localization presaged the study of coherence and “reproducible noise” or chaos. Source of motivation in 1957: Microscopic nature of irreversibility. Could coherence prevent quantum transport? (Note Azbel’s emphasis on reproducible noise in σ of small samples.)
This is the essence of many beautiful experiments on weak localization —coherence can weaken or even enhance quantum transport. Spin orbit scattering reverses phases (Fukuyama, Bergmann, Dynes, and Bishop). Oscillatory phenomena: Sharvin and Sharvin, etc. In sum: “We can no longer doubt the fact of interference modulation of transport processes no matter how much we may dispute the details of the metal insulator transition”.
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(c)
A neglected area: Non-electrical analogues, e.g., propagation of light in fogs + pigments, sound in random media, etc. When diffusive, reflective, transmitting? Role of conservation laws. Some ill-conceived work on excitons and on phonons in random media, but no conclusive work. One might name this field “dirty bosons”: It is relevant, for instance, to many phase-transition problems.
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Work done at Princeton University supported in part by NSF Grant DMR 8020263
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© 1985 Springer-Verlag Berlin Heidelberg
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Anderson, P.W. (1985). Some Unresolved Questions in the Theory of Localization. In: Kramer, B., Bergmann, G., Bruynseraede, Y. (eds) Localization, Interaction, and Transport Phenomena. Springer Series in Solid-State Sciences, vol 61. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-82516-3_2
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