Topological Dimensions from Disorder and Quantum Mechanics?

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

Topological Dimensions from Disorder and Quantum Mechanics?

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

Topological Dimensions from Disorder and Quantum Mechanics?

Popis výsledku anglicky

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.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

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

Projekt

—

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2023

Kód důvěrnosti údajů

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

Název periodika

Entropy

ISSN

1099-4300

e-ISSN

1099-4300

Svazek periodika

25

Číslo periodika v rámci svazku

11

Stát vydavatele periodika

CH - Švýcarská konfederace

Počet stran výsledku

9

Strana od-do

1557

Kód UT WoS článku

001118370500001

EID výsledku v databázi Scopus

2-s2.0-85178142533