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arXiv · 2207.13569

Low-Dimensional Life of Critical Anderson Electron

Ivan Horváth·Peter Markoš
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Abstract

We show that critical Anderson electron in 3 dimensions is present in its spatial effective support, which was recently determined to be a region of fractal dimension $\approx \! 8/3$, with probability 1 in infinite volume. Hence, its physics is fully confined to space of this lower dimension. Stated differently, effective description of space occupied by critical Anderson electron becomes a full description in infinite volume. We then show that it is a general feature of the effective counting dimension underlying these concepts, that its subnominal value implies an exact description by effective support.

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Ivan Horváth, Peter Markoš. 2022-07-27. Low-Dimensional Life of Critical Anderson Electron. https://doi.org/10.1016/j.physleta.2023.128735

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