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Topological Dimensions from Disorder and Quantum Mechanics?
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SYSNO ASEP 0579732 Druh ASEP J - Článek v odborném periodiku Zařazení RIV J - Článek v odborném periodiku Poddruh J Článek ve WOS Název Topological Dimensions from Disorder and Quantum Mechanics? Tvůrce(i) Horváth, Ivan (UJF-V) ORCID, SAI
Markoš, P. (SK)Celkový počet autorů 2 Číslo článku 1557 Zdroj.dok. Entropy. - : MDPI
Roč. 25, č. 11 (2023)Poč.str. 9 s. Forma vydání Online - E Jazyk dok. eng - angličtina Země vyd. CH - Švýcarsko Klíč. slova Anderson transition ; localization ; effective counting dimension ; effective number theory ; effective support ; dimension contentemergent space Obor OECD Atomic, molecular and chemical physics (physics of atoms and molecules including collision, interaction with radiation, magnetic resonances, Mössbauer effect) Způsob publikování Open access Institucionální podpora UJF-V - RVO:61389005 UT WOS 001118370500001 EID SCOPUS 85178142533 DOI 10.3390/e25111557 Anotace 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. Pracoviště Ústav jaderné fyziky Kontakt Markéta Sommerová, sommerova@ujf.cas.cz, Tel.: 266 173 228 Rok sběru 2024 Elektronická adresa https://doi.org/10.3390/e25111557
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