FRINK Linked Data Fragments server

Matches in SemOpenAlex for { <https://semopenalex.org/work/W4223653865> ?p ?o ?g. }

• W4223653865 endingPage "4148" @default.
• W4223653865 startingPage "4131" @default.
• W4223653865 abstract "Abstract In this paper, we consider Schrödinger operators on $$Mtimes {mathbb {Z}}^{d_{2}}$$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:mrow> <mml:mi>M</mml:mi> <mml:mo>×</mml:mo> <mml:msup> <mml:mrow> <mml:mi>Z</mml:mi> </mml:mrow> <mml:msub> <mml:mi>d</mml:mi> <mml:mn>2</mml:mn> </mml:msub> </mml:msup> </mml:mrow> </mml:math> , with $$M={M_{1},ldots ,M_{2}}^{d_{1}}$$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:mrow> <mml:mi>M</mml:mi> <mml:mo>=</mml:mo> <mml:msup> <mml:mrow> <mml:mo>{</mml:mo> <mml:msub> <mml:mi>M</mml:mi> <mml:mn>1</mml:mn> </mml:msub> <mml:mo>,</mml:mo> <mml:mo>…</mml:mo> <mml:mo>,</mml:mo> <mml:msub> <mml:mi>M</mml:mi> <mml:mn>2</mml:mn> </mml:msub> <mml:mo>}</mml:mo> </mml:mrow> <mml:msub> <mml:mi>d</mml:mi> <mml:mn>1</mml:mn> </mml:msub> </mml:msup> </mml:mrow> </mml:math> (‘quantum wave guides’) with a ‘ $$Gamma $$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:mi>Γ</mml:mi> </mml:math> -trimmed’ random potential, namely a potential which vanishes outside a subset $$Gamma $$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:mi>Γ</mml:mi> </mml:math> which is periodic with respect to a sub-lattice. We prove that (under appropriate assumptions) for strong disorder these operators have pure point spectrum outside the set $$Sigma _{0}=sigma (H_{0,Gamma ^{c}})$$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:mrow> <mml:msub> <mml:mi>Σ</mml:mi> <mml:mn>0</mml:mn> </mml:msub> <mml:mo>=</mml:mo> <mml:mi>σ</mml:mi> <mml:mrow> <mml:mo>(</mml:mo> <mml:msub> <mml:mi>H</mml:mi> <mml:mrow> <mml:mn>0</mml:mn> <mml:mo>,</mml:mo> <mml:msup> <mml:mi>Γ</mml:mi> <mml:mi>c</mml:mi> </mml:msup> </mml:mrow> </mml:msub> <mml:mo>)</mml:mo> </mml:mrow> </mml:mrow> </mml:math> where $$H_{0,Gamma ^{c}} $$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:msub> <mml:mi>H</mml:mi> <mml:mrow> <mml:mn>0</mml:mn> <mml:mo>,</mml:mo> <mml:msup> <mml:mi>Γ</mml:mi> <mml:mi>c</mml:mi> </mml:msup> </mml:mrow> </mml:msub> </mml:math> is the free (discrete) Laplacian on the complement $$Gamma ^{c} $$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:msup> <mml:mi>Γ</mml:mi> <mml:mi>c</mml:mi> </mml:msup> </mml:math> of $$Gamma $$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:mi>Γ</mml:mi> </mml:math> . We also prove that the operators have some absolutely continuous spectrum in an energy region $${mathcal {E}}subset Sigma _{0}$$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:mrow> <mml:mi>E</mml:mi> <mml:mo>⊂</mml:mo> <mml:msub> <mml:mi>Σ</mml:mi> <mml:mn>0</mml:mn> </mml:msub> </mml:mrow> </mml:math> . Consequently, there is a mobility edge for such models. We also consider the case $$-M_{1}=M_{2}=infty $$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:mrow> <mml:mo>-</mml:mo> <mml:msub> <mml:mi>M</mml:mi> <mml:mn>1</mml:mn> </mml:msub> <mml:mo>=</mml:mo> <mml:msub> <mml:mi>M</mml:mi> <mml:mn>2</mml:mn> </mml:msub> <mml:mo>=</mml:mo> <mml:mi>∞</mml:mi> </mml:mrow> </mml:math> , i.e. $$Gamma $$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:mi>Γ</mml:mi> </mml:math> -trimmed operators on $${mathbb {Z}}^{d}={mathbb {Z}}^{d_{1}}times {mathbb {Z}}^{d_{2}}$$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:mrow> <mml:msup> <mml:mrow> <mml:mi>Z</mml:mi> </mml:mrow> <mml:mi>d</mml:mi> </mml:msup> <mml:mo>=</mml:mo> <mml:msup> <mml:mrow> <mml:mi>Z</mml:mi> </mml:mrow> <mml:msub> <mml:mi>d</mml:mi> <mml:mn>1</mml:mn> </mml:msub> </mml:msup> <mml:mo>×</mml:mo> <mml:msup> <mml:mrow> <mml:mi>Z</mml:mi> </mml:mrow> <mml:msub> <mml:mi>d</mml:mi> <mml:mn>2</mml:mn> </mml:msub> </mml:msup> </mml:mrow> </mml:math> . Again, we prove localisation outside $$Sigma _{0} $$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:msub> <mml:mi>Σ</mml:mi> <mml:mn>0</mml:mn> </mml:msub> </mml:math> by showing exponential decay of the Green function $$G_{E+ieta }(x,y) $$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:mrow> <mml:msub> <mml:mi>G</mml:mi> <mml:mrow> <mml:mi>E</mml:mi> <mml:mo>+</mml:mo> <mml:mi>i</mml:mi> <mml:mi>η</mml:mi> </mml:mrow> </mml:msub> <mml:mrow> <mml:mo>(</mml:mo> <mml:mi>x</mml:mi> <mml:mo>,</mml:mo> <mml:mi>y</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> </mml:mrow> </mml:math> uniformly in $$eta >0 $$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:mrow> <mml:mi>η</mml:mi> <mml:mo>></mml:mo> <mml:mn>0</mml:mn> </mml:mrow> </mml:math> . For all energies $$Ein {mathcal {E}}$$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:mrow> <mml:mi>E</mml:mi> <mml:mo>∈</mml:mo> <mml:mi>E</mml:mi> </mml:mrow> </mml:math> we prove that the Green’s function $$G_{E+ieta } $$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:msub> <mml:mi>G</mml:mi> <mml:mrow> <mml:mi>E</mml:mi> <mml:mo>+</mml:mo> <mml:mi>i</mml:mi> <mml:mi>η</mml:mi> </mml:mrow> </mml:msub> </mml:math> is not (uniformly) in $$ell ^{1}$$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:msup> <mml:mi>ℓ</mml:mi> <mml:mn>1</mml:mn> </mml:msup> </mml:math> as $$eta $$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:mi>η</mml:mi> </mml:math> approaches 0. This implies that neither the fractional moment method nor multi-scale analysis can be applied here." @default.
• W4223653865 created "2022-04-15" @default.
• W4223653865 creator A5010224305 @default.
• W4223653865 creator A5072102712 @default.
• W4223653865 date "2022-04-10" @default.
• W4223653865 modified "2023-10-05" @default.
• W4223653865 title "Localisation and Delocalisation for a Simple Quantum Wave Guide with Randomness" @default.
• W4223653865 cites W149533326 @default.
• W4223653865 cites W1965138981 @default.
• W4223653865 cites W2032086015 @default.
• W4223653865 cites W2042805020 @default.
• W4223653865 cites W2044270536 @default.
• W4223653865 cites W2050140134 @default.
• W4223653865 cites W2084359832 @default.
• W4223653865 cites W2087671737 @default.
• W4223653865 cites W2089165964 @default.
• W4223653865 cites W2099820850 @default.
• W4223653865 cites W2166746313 @default.
• W4223653865 cites W2962804829 @default.
• W4223653865 cites W3026221619 @default.
• W4223653865 cites W3104061455 @default.
• W4223653865 cites W3105317875 @default.
• W4223653865 cites W3123870927 @default.
• W4223653865 cites W4212986001 @default.
• W4223653865 cites W4234290203 @default.
• W4223653865 cites W4234905640 @default.
• W4223653865 cites W4248744331 @default.
• W4223653865 doi "https://doi.org/10.1007/s00023-022-01177-x" @default.
• W4223653865 hasPublicationYear "2022" @default.
• W4223653865 type Work @default.
• W4223653865 citedByCount "0" @default.
• W4223653865 crossrefType "journal-article" @default.
• W4223653865 hasAuthorship W4223653865A5010224305 @default.
• W4223653865 hasAuthorship W4223653865A5072102712 @default.
• W4223653865 hasBestOaLocation W42236538651 @default.
• W4223653865 hasConcept C11413529 @default.
• W4223653865 hasConcept C41008148 @default.
• W4223653865 hasConceptScore W4223653865C11413529 @default.
• W4223653865 hasConceptScore W4223653865C41008148 @default.
• W4223653865 hasIssue "11" @default.
• W4223653865 hasLocation W42236538651 @default.
• W4223653865 hasOpenAccess W4223653865 @default.
• W4223653865 hasPrimaryLocation W42236538651 @default.
• W4223653865 hasRelatedWork W2051487156 @default.
• W4223653865 hasRelatedWork W2052122378 @default.
• W4223653865 hasRelatedWork W2053286651 @default.
• W4223653865 hasRelatedWork W2073681303 @default.
• W4223653865 hasRelatedWork W2317200988 @default.
• W4223653865 hasRelatedWork W2544423928 @default.
• W4223653865 hasRelatedWork W2947381795 @default.
• W4223653865 hasRelatedWork W2181413294 @default.
• W4223653865 hasRelatedWork W2181743346 @default.
• W4223653865 hasRelatedWork W2187401768 @default.
• W4223653865 hasVolume "23" @default.
• W4223653865 isParatext "false" @default.
• W4223653865 isRetracted "false" @default.
• W4223653865 workType "article" @default.