Sie befinden Sich nicht im Netzwerk der Universität Paderborn. Der Zugriff auf elektronische Ressourcen ist gegebenenfalls nur via VPN oder Shibboleth (DFN-AAI) möglich. mehr Informationen...
Ergebnis 14 von 227
SciPost physics, 2021-04, Vol.10 (4), p.082, Article 082
2021

Details

Autor(en) / Beteiligte
Titel
Impurities in systems of noninteracting trapped fermions
Ist Teil von
  • SciPost physics, 2021-04, Vol.10 (4), p.082, Article 082
Ort / Verlag
SciPost Foundation
Erscheinungsjahr
2021
Link zum Volltext
Quelle
EZB Electronic Journals Library
Beschreibungen/Notizen
  • We study the properties of spin-less non-interacting fermions trapped in a confining potential in one dimension but in the presence of one or more impurities which are modelled by delta function potentials. We use a method based on the single particle Green's function. For a single impurity placed in the bulk, we compute the density of the Fermi gas near the impurity. Our results, in addition to recovering the Friedel oscillations at large distance from the impurity, allow the exact computation of the density at short distances. We also show how the density of the Fermi gas is modified when the impurity is placed near the edge of the trap in the region where the unperturbed system is described by the Airy gas. Our method also allows us to compute the effective potential felt by the impurity both in the bulk and at the edge. In the bulk this effective potential is shown to be a universal function only of the local Fermi wave vector, or equivalently of the local fermion density. When the impurity is placed near the edge of the Fermi gas, the effective potential can be expressed in terms of Airy functions. For an attractive impurity placed far outside the support of the fermion density, we show that an interesting transition occurs where a single fermion is pulled out of the Fermi sea and forms a bound state with the impurity. This is a quantum analogue of the well-known Baik-Ben Arous-Péché (BBP) transition, known in the theory of spiked random matrices. The density at the location of the impurity plays the role of an order parameter. We also consider the case of two impurities in the bulk and compute exactly the effective force between them mediated by the background Fermi gas.
Sprache
Englisch
Identifikatoren
ISSN: 2542-4653
eISSN: 2542-4653
DOI: 10.21468/SciPostPhys.10.4.082
Titel-ID: cdi_doaj_primary_oai_doaj_org_article_9a465bf8adc24e21a10dcab550fa2902
Format
Schlagworte
Physics

Weiterführende Literatur

Empfehlungen zum selben Thema automatisch vorgeschlagen von bX