Matches in SemOpenAlex for { <https://semopenalex.org/work/W3106508749> ?p ?o ?g. }
Showing items 1 to 63 of
63
with 100 items per page.
- W3106508749 abstract "We study the one-dimensional random dimer model, with Hamiltonian $H_omega=Delta + V_omega$, where for all $xinZ, V_omega(2x)=V_omega(2x+1)$ and where the $V_omega(2x)$ are i.i.d. Bernoulli random variables taking the values $pm V, V>0$. We show that, for all values of $V$ and with probability one in $omega$, the spectrum of $H$ is pure point. If $Vleq1$ and $Vneq 1/sqrt{2}$, the Lyapounov exponent vanishes only at the two critical energies given by $E=pm V$. For the particular value $V=1/sqrt{2}$, respectively $V=sqrt{2}$, we show the existence of additional critical energies at $E=pm 3/sqrt{2}$, resp. E=0. On any compact interval $I$ not containing the critical energies, the eigenfunctions are then shown to be semi-uniformly exponentially localized, and this implies dynamical localization: for all $q>0$ and for all $psiinell^2(Z)$ with sufficiently rapid decrease: $$ sup_t r^{(q)}_{psi,I}(t) equiv sup_t < P_I(H_omega)psi_t, |X|^q P_I(H_omega)psi_t > <infty. $$ Here $psi_t=e^{-iH_omega t} psi$, and $P_I(H_omega)$ is the spectral projector of $H_omega$ onto the interval $I$. In particular if $V>1$ and $Vneq sqrt{2}$, these results hold on the entire spectrum (so that one can take $I=sigma(H_omega)$)." @default.
- W3106508749 created "2020-11-23" @default.
- W3106508749 creator A5039159360 @default.
- W3106508749 creator A5091262946 @default.
- W3106508749 date "2000-01-01" @default.
- W3106508749 modified "2023-10-15" @default.
- W3106508749 title "Dynamical Localization for the Random Dimer Model" @default.
- W3106508749 cites W1595019369 @default.
- W3106508749 cites W1600977221 @default.
- W3106508749 cites W1674638202 @default.
- W3106508749 cites W1965138981 @default.
- W3106508749 cites W1973741257 @default.
- W3106508749 cites W1982332624 @default.
- W3106508749 cites W1985435912 @default.
- W3106508749 cites W1992567833 @default.
- W3106508749 cites W1995812256 @default.
- W3106508749 cites W2004240279 @default.
- W3106508749 cites W2015009177 @default.
- W3106508749 cites W2040423578 @default.
- W3106508749 cites W2059121108 @default.
- W3106508749 cites W2061627154 @default.
- W3106508749 cites W2072804782 @default.
- W3106508749 cites W2079036331 @default.
- W3106508749 cites W2798461040 @default.
- W3106508749 cites W3015754474 @default.
- W3106508749 hasPublicationYear "2000" @default.
- W3106508749 type Work @default.
- W3106508749 sameAs 3106508749 @default.
- W3106508749 citedByCount "38" @default.
- W3106508749 countsByYear W31065087492015 @default.
- W3106508749 countsByYear W31065087492016 @default.
- W3106508749 countsByYear W31065087492017 @default.
- W3106508749 countsByYear W31065087492019 @default.
- W3106508749 countsByYear W31065087492020 @default.
- W3106508749 countsByYear W31065087492022 @default.
- W3106508749 crossrefType "journal-article" @default.
- W3106508749 hasAuthorship W3106508749A5039159360 @default.
- W3106508749 hasAuthorship W3106508749A5091262946 @default.
- W3106508749 hasBestOaLocation W31065087492 @default.
- W3106508749 hasConcept C121332964 @default.
- W3106508749 hasConcept C2779546866 @default.
- W3106508749 hasConcept C46141821 @default.
- W3106508749 hasConceptScore W3106508749C121332964 @default.
- W3106508749 hasConceptScore W3106508749C2779546866 @default.
- W3106508749 hasConceptScore W3106508749C46141821 @default.
- W3106508749 hasLocation W31065087491 @default.
- W3106508749 hasLocation W31065087492 @default.
- W3106508749 hasOpenAccess W3106508749 @default.
- W3106508749 hasPrimaryLocation W31065087491 @default.
- W3106508749 hasRelatedWork W2045358690 @default.
- W3106508749 hasRelatedWork W2048336437 @default.
- W3106508749 hasRelatedWork W2059165039 @default.
- W3106508749 hasRelatedWork W2087297363 @default.
- W3106508749 hasRelatedWork W2095007762 @default.
- W3106508749 hasRelatedWork W2269777559 @default.
- W3106508749 hasRelatedWork W2331188555 @default.
- W3106508749 hasRelatedWork W2800653904 @default.
- W3106508749 hasRelatedWork W2953262987 @default.
- W3106508749 hasRelatedWork W4302613702 @default.
- W3106508749 isParatext "false" @default.
- W3106508749 isRetracted "false" @default.
- W3106508749 magId "3106508749" @default.
- W3106508749 workType "article" @default.