Topological Dimensions from Disorder and Quantum Mechanics?

0579732 - ÚJF 2024 RIV CH eng J - Journal Article
Horváth, Ivan - Markoš, P.
Topological Dimensions from Disorder and Quantum Mechanics?
Entropy. Roč. 25, č. 11 (2023), č. článku 1557. E-ISSN 1099-4300
Institutional support: RVO:61389005
Keywords : Anderson transition * localization * effective counting dimension * effective number theory * effective support * dimension contentemergent space
OECD category: Atomic, molecular and chemical physics (physics of atoms and molecules including collision, interaction with radiation, magnetic resonances, Mössbauer effect)
Impact factor: 2.7, year: 2022
Method of publishing: Open access
https://doi.org/10.3390/e25111557

We have recently shown that the critical Anderson electron in D=3 dimensions effectively occupies a spatial region of the infrared (IR) scaling dimension dIR approximate to 8/3. Here, we inquire about the dimensional substructure involved. We partition space into regions of equal quantum occurrence probabilities, such that the points comprising a region are of similar relevance, and calculate the IR scaling dimension d of each. This allows us to infer the probability density p(d) for dimension d to be accessed by the electron. We find that p(d) has a strong peak at d very close to two. In fact, our data suggest that p(d) is non-zero on the interval [dmin,dmax]approximate to[4/3,8/3] and may develop a discrete part (delta-function) at d=2 in the infinite-volume limit. The latter invokes the possibility that a combination of quantum mechanics and pure disorder can lead to the emergence of integer (topological) dimensions. Although dIR is based on effective counting, of which p(d) has no a priori knowledge, dIR >= dmax is an exact feature of the ensuing formalism. A possible connection of our results to the recent findings of dIR approximate to 2 in Dirac near-zero modes of thermal quantum chromodynamics is emphasized.
Permanent Link: https://hdl.handle.net/11104/0348534