Quantum systems at the brink: existence of bound states, critical potentials, and dimensionality
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21340%2F23%3A00367521" target="_blank" >RIV/68407700:21340/23:00367521 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1017/fms.2023.39" target="_blank" >https://doi.org/10.1017/fms.2023.39</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1017/fms.2023.39" target="_blank" >10.1017/fms.2023.39</a>
Alternative languages
Result language
angličtina
Original language name
Quantum systems at the brink: existence of bound states, critical potentials, and dimensionality
Original language description
One of the crucial properties of a quantum system is the existence of bound states. While the existence of eigenvalues below zero, that is, below the essential spectrum, is well understood, the situation of zero energy bound states at the edge of the essential spectrum is far less understood. We present complementary sharp criteria for the existence and nonexistence of zero energy ground states. Our criteria give a straightforward explanation for the folklore that there is a spectral phase transition with critical dimension four, concerning the existence versus nonexistence of zero energy ground states.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10100 - Mathematics
Result continuities
Project
—
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2023
Confidentiality
C - Předmět řešení projektu podléhá obchodnímu tajemství (§ 504 Občanského zákoníku), ale název projektu, cíle projektu a u ukončeného nebo zastaveného projektu zhodnocení výsledku řešení projektu (údaje P03, P04, P15, P19, P29, PN8) dodané do CEP, jsou upraveny tak, aby byly zveřejnitelné.
Data specific for result type
Name of the periodical
Forum of Mathematics, Sigma
ISSN
2050-5094
e-ISSN
2050-5094
Volume of the periodical
11
Issue of the periodical within the volume
e61
Country of publishing house
GB - UNITED KINGDOM
Number of pages
29
Pages from-to
1-29
UT code for WoS article
001029742200001
EID of the result in the Scopus database
2-s2.0-85166434641