Low-Dimensional Life of Critical Anderson Electron
arXiv:2207.13569 · doi:10.1016/j.physleta.2023.128735
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 , 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.
4 pages, 2 figures; v2: fixes minor glitches; v3: published version
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