What question did this study set out to answer?

To determine whether zero-temperature electronic conductance in disordered systems follows a universal dependence on sample length scale across different spatial dimensions.

March 5, 1979Physical Review Letters

Scaling Theory of Localization: Absence of Quantum Diffusion in Two Dimensions

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Authors

EAElihu AbrahamsUniversité Paris-Sud PAPhilip W. AndersonRutgers, The State University of New Jersey DLD. C. LicciardelloPrinceton University

Discussion

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Implication

Theoretical analysis reveals absence of true metallic behavior in two dimensions, indicating universal scaling limits quantum diffusion in disordered systems.

Key Points

To determine whether zero-temperature electronic conductance in disordered systems follows a universal dependence on sample length scale across different spatial dimensions.
Formulated a single-parameter scaling hypothesis relating zero-temperature conductance to system length scale.
Derived asymptotic forms for the continuous scaling function beta(G) = d(ln G)/d(ln L) in limits far above and below critical conductance.
In three dimensions, the critical conductance acts as an unstable fixed point separating metallic states from insulating localized states.
In two dimensions, true metallic behavior is absent as conductance decreases monotonically with length scale, shifting smoothly from a logarithmic drop to an exponential decay.

Cite This Study

Abrahams et al. (1979) studied this question.

synapsesocial.com/papers/696f16bd759b097567377a16 https://doi.org/10.1103/physrevlett.42.673

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March 5, 1979Physical Review Letters

Scaling Theory of Localization: Absence of Quantum Diffusion in Two Dimensions

View Full Paper

Ask AI

Bookmark

Authors

EAElihu AbrahamsUniversité Paris-Sud PAPhilip W. AndersonRutgers, The State University of New Jersey DLD. C. LicciardelloPrinceton University

Discussion

Member takes

Implication

Theoretical analysis reveals absence of true metallic behavior in two dimensions, indicating universal scaling limits quantum diffusion in disordered systems.

Key Points

To determine whether zero-temperature electronic conductance in disordered systems follows a universal dependence on sample length scale across different spatial dimensions.
Formulated a single-parameter scaling hypothesis relating zero-temperature conductance to system length scale.
Derived asymptotic forms for the continuous scaling function beta(G) = d(ln G)/d(ln L) in limits far above and below critical conductance.
In three dimensions, the critical conductance acts as an unstable fixed point separating metallic states from insulating localized states.
In two dimensions, true metallic behavior is absent as conductance decreases monotonically with length scale, shifting smoothly from a logarithmic drop to an exponential decay.

Cite This Study

Abrahams et al. (1979) studied this question.

synapsesocial.com/papers/696f16bd759b097567377a16 https://doi.org/10.1103/physrevlett.42.673

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