Universal conductance fluctuations in non-integer dimensions

Details Universal conductance fluctuations in non-integer dimensions Universal conductance fluctuations in non-integer dimensions

2003-06-03

arxiv.org/abs/cond-mat/0306064v1

Physics

Condensed Matter

Disordered Systems and Neural Networks

4 pages, 4 figures submitted to Phys. Rev.B

Scientific paper

10.1103/PhysRevB.69.033104

We propose an Ansatz for Universal conductance fluctuations in continuous dimensions from 0 up to 4. The Ansatz agrees with known formulas for integer dimensions 1, 2 and 3, both for hard wall and periodic boundary conditions. The method is based solely on the knowledge of energy spectrum and standard assumptions. We also study numerically the conductance fluctuations in 4D Anderson model, depending on system size L and disorder W. We find a small plateau with a value diverging logarithmically with increasing L. Universality gets lost just in 4D.

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