Topological Dimensions from Disorder and Quantum Mechanics?

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61389005%3A_____%2F23%3A00579732" target="_blank" >RIV/61389005:_____/23:00579732 - isvavai.cz</a>

Result on the web

<a href="https://doi.org/10.3390/e25111557" target="_blank" >https://doi.org/10.3390/e25111557</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.3390/e25111557" target="_blank" >10.3390/e25111557</a>

Result language

angličtina

Original language name

Topological Dimensions from Disorder and Quantum Mechanics?

Original language description

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.

Czech name

—

Czech description

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Type

J_imp - Article in a specialist periodical, which is included in the Web of Science database

CEP classification

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OECD FORD branch

10301 - Atomic, molecular and chemical physics (physics of atoms and molecules including collision, interaction with radiation, magnetic resonances, Mössbauer effect)

Project

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Continuities

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year

2023

Confidentiality

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Name of the periodical

Entropy

ISSN

1099-4300

e-ISSN

1099-4300

Volume of the periodical

25

Issue of the periodical within the volume

11

Country of publishing house

CH - SWITZERLAND

Number of pages

9

Pages from-to

1557

UT code for WoS article

001118370500001

EID of the result in the Scopus database

2-s2.0-85178142533