Scaling Theory of Localization: Absence of Quantum Diffusion in Two Dimensions
1979/03/05 by Elihu Abrahams, Philip W. Anderson, D. C. Licciardello +1 · 6,138 citations
Mathematics · Physics and Astronomy · #Condensed matter physics #Conductance #Diffusion #Exponential function #Function (biology) #Geometry #Logarithm #Mathematical analysis #Mathematical physics #Mathematics #Physics #Quantum and electron transport phenomena #Quantum mechanics #Scaling #Surface and Thin Film Phenomena #Theoretical and Computational Physics
paper · doi:10.1103/physrevlett.42.673
published in Physical Review Letters 42(10), 673-676 (American Physical Society)
openalex publication_date 1979/03/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/04
Abstract
Arguments are presented that the T=0 conductance G of a disordered electronic system depends on its length scale L in a universal manner. Asymptotic forms are obtained for the scaling function \ensuremathβ(G)=(dlnG)/(dlnL), valid for both G\ensuremath≪Gc\ensuremath≃\frace2\ensuremathℏ and G\ensuremath≫Gc. In three dimensions, Gc is an unstable fixed point. In two dimensions, there is no true metallic behavior; the conductance crosses over smoothly from logarithmic or slower to exponential decrease with L.
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- Elihu Abrahams [wikipedia]