Aharonov and Bohm versus Welsh eigenvalues
We consider a class of two-dimensional Schrödinger operator with a singular interaction of the δ type and a fixed strength β supported by an infinite family of concentric, equidistantly spaced circles, and discuss what happens below the essential spectrum when the system is amended by an Aharonov-Bohm flux α∈[0,12] in the center. It is shown that if β≠0 , there is a critical value αcrit∈(0,12) such that the discrete spectrum has an accumulation point when α<αcrit , while for α≥αcrit the number of eigenvalues is at most finite, in particular, the discrete spectrum is empty for any fixed α∈(0,12) and |β| small enough.
| Medienart: |
E-Artikel |
|---|
| Erscheinungsjahr: |
2018 |
|---|---|
| Erschienen: |
2018 |
| Enthalten in: |
Zur Gesamtaufnahme - volume:108 |
|---|---|
| Enthalten in: |
Letters in mathematical physics - 108(2018), 9 vom: 20., Seite 2153-2167 |
| Sprache: |
Englisch |
|---|
| Beteiligte Personen: |
|---|
| Links: |
|---|
| Themen: |
Aharonov–Bohm flux |
|---|
| Anmerkungen: |
Date Revised 30.09.2020 published: Print-Electronic Citation Status PubMed-not-MEDLINE |
|---|
| doi: |
10.1007/s11005-018-1069-9 |
|---|
| funding: |
|
|---|---|
| Förderinstitution / Projekttitel: |
|
| PPN (Katalog-ID): |
NLM287396665 |
|---|
| LEADER | 01000naa a22002652 4500 | ||
|---|---|---|---|
| 001 | NLM287396665 | ||
| 003 | DE-627 | ||
| 005 | 20231225053922.0 | ||
| 007 | cr uuu---uuuuu | ||
| 008 | 231225s2018 xx |||||o 00| ||eng c | ||
| 024 | 7 | |a 10.1007/s11005-018-1069-9 |2 doi | |
| 028 | 5 | 2 | |a pubmed24n0957.xml |
| 035 | |a (DE-627)NLM287396665 | ||
| 035 | |a (NLM)30100669 | ||
| 040 | |a DE-627 |b ger |c DE-627 |e rakwb | ||
| 041 | |a eng | ||
| 100 | 1 | |a Exner, P |e verfasserin |4 aut | |
| 245 | 1 | 0 | |a Aharonov and Bohm versus Welsh eigenvalues |
| 264 | 1 | |c 2018 | |
| 336 | |a Text |b txt |2 rdacontent | ||
| 337 | |a ƒaComputermedien |b c |2 rdamedia | ||
| 338 | |a ƒa Online-Ressource |b cr |2 rdacarrier | ||
| 500 | |a Date Revised 30.09.2020 | ||
| 500 | |a published: Print-Electronic | ||
| 500 | |a Citation Status PubMed-not-MEDLINE | ||
| 520 | |a We consider a class of two-dimensional Schrödinger operator with a singular interaction of the δ type and a fixed strength β supported by an infinite family of concentric, equidistantly spaced circles, and discuss what happens below the essential spectrum when the system is amended by an Aharonov-Bohm flux α∈[0,12] in the center. It is shown that if β≠0 , there is a critical value αcrit∈(0,12) such that the discrete spectrum has an accumulation point when α<αcrit , while for α≥αcrit the number of eigenvalues is at most finite, in particular, the discrete spectrum is empty for any fixed α∈(0,12) and |β| small enough | ||
| 650 | 4 | |a Journal Article | |
| 650 | 4 | |a Aharonov–Bohm flux | |
| 650 | 4 | |a Discrete spectrum | |
| 650 | 4 | |a Radial symmetry | |
| 650 | 4 | |a Singular Schrödinger operator | |
| 700 | 1 | |a Kondej, S |e verfasserin |4 aut | |
| 773 | 0 | 8 | |i Enthalten in |t Letters in mathematical physics |d 2017 |g 108(2018), 9 vom: 20., Seite 2153-2167 |w (DE-627)NLM277388589 |x 1573-0530 |7 nnns |
| 773 | 1 | 8 | |g volume:108 |g year:2018 |g number:9 |g day:20 |g pages:2153-2167 |
| 856 | 4 | 0 | |u http://dx.doi.org/10.1007/s11005-018-1069-9 |3 Volltext |
| 912 | |a GBV_USEFLAG_A | ||
| 912 | |a GBV_NLM | ||
| 951 | |a AR | ||
| 952 | |d 108 |j 2018 |e 9 |b 20 |h 2153-2167 | ||