TY - JOUR

T1 - Quantum diffusion and localization in disordered systems

AU - Kaveh, M.

PY - 1985/4

Y1 - 1985/4

N2 - We describe quantum diffusion of the electrons in a disordered system by requiring that ψ(r, t)2 obeys a diffusion equation, where ψ(r, t) is the time-dependent wavefunction. It is found that, regardless of the weakness of the disorder, this requirement leads to electron eigenstates which consist of a power-law component for dimension d> 1 and a logarithmic correction for d = 1, in addition to an extended function. For d≤2, this is correct only below a certain length scale. As a result, even for kFl>>1, the conductivity σ is reduced from the Boltzmann conductivity σB in agreement with diagrammatic calculations. By expanding the eigenstate in terms of 1/rnit is shown that the 1 /rd−1 term is responsible for the reduction of σ in the weak-disorder limit. It is demonstrated that in three dimensions one can extrapolate the formula for the conductivity down to the Anderson transition to obtain σ =g2σB[1−(C/g2kF2l2) (1 − l/L)] where g is the reduction in the density of states due to disorder and C is a dimensionless constant of order unity which depends on some cut-off length.

AB - We describe quantum diffusion of the electrons in a disordered system by requiring that ψ(r, t)2 obeys a diffusion equation, where ψ(r, t) is the time-dependent wavefunction. It is found that, regardless of the weakness of the disorder, this requirement leads to electron eigenstates which consist of a power-law component for dimension d> 1 and a logarithmic correction for d = 1, in addition to an extended function. For d≤2, this is correct only below a certain length scale. As a result, even for kFl>>1, the conductivity σ is reduced from the Boltzmann conductivity σB in agreement with diagrammatic calculations. By expanding the eigenstate in terms of 1/rnit is shown that the 1 /rd−1 term is responsible for the reduction of σ in the weak-disorder limit. It is demonstrated that in three dimensions one can extrapolate the formula for the conductivity down to the Anderson transition to obtain σ =g2σB[1−(C/g2kF2l2) (1 − l/L)] where g is the reduction in the density of states due to disorder and C is a dimensionless constant of order unity which depends on some cut-off length.

UR - http://www.scopus.com/inward/record.url?scp=0022042878&partnerID=8YFLogxK

U2 - 10.1080/13642818508240591

DO - 10.1080/13642818508240591

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AN - SCOPUS:0022042878

SN - 1364-2812

VL - 51

SP - 453

EP - 464

JO - Philosophical Magazine B: Physics of Condensed Matter; Statistical Mechanics, Electronic, Optical and Magnetic Properties

JF - Philosophical Magazine B: Physics of Condensed Matter; Statistical Mechanics, Electronic, Optical and Magnetic Properties

IS - 4

ER -