Eigenstates and instabilities of chains with embedded defects (Articolo in rivista)

Type
Label
  • Eigenstates and instabilities of chains with embedded defects (Articolo in rivista) (literal)
Anno
  • 2013-01-01T00:00:00+01:00 (literal)
Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#doi
  • 10.1063/1.4803523 (literal)
Alternative label
  • J. D'Ambroise (1); P.G. Kevrekidis (2); S. Lepri (3) (2013)
    Eigenstates and instabilities of chains with embedded defects
    in Chaos (Woodbury N.Y.)
    (literal)
Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#autori
  • J. D'Ambroise (1); P.G. Kevrekidis (2); S. Lepri (3) (literal)
Pagina inizio
  • art_n_023109 (literal)
Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#url
  • http://scitation.aip.org/content/aip/journal/chaos/23/2/10.1063/1.4803523 (literal)
Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#numeroVolume
  • 23 (literal)
Rivista
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  • 2 (literal)
Note
  • PubMe (literal)
Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#affiliazioni
  • (1) Department of Mathematics, Bard College, Annandale-on-Hudson, New York 12504, USA (2) Department of Mathematics and Statistics, University of Massachusetts, Amherst, Massachusetts 01003-4515, USA (3) CNR-Consiglio Nazionale delle Ricerche, Istituto dei Sistemi Complessi, via Madonna del piano 10, I-50019 Sesto Fiorentino, Italy (literal)
Titolo
  • Eigenstates and instabilities of chains with embedded defects (literal)
Abstract
  • We consider the eigenvalue problem for one-dimensional linear Schro?dinger lattices (tight-binding) with an embedded few-sites linear or nonlinear, Hamiltonian or non-conservative defect (an oligomer). Such a problem arises when considering scattering states in the presence of (generally complex) impurities as well as in the stability analysis of nonlinear waves. We describe a general approach based on a matching of solutions of the linear portions of the lattice at the location of the oligomer defect. As specific examples, we discuss both linear and nonlinear, Hamiltonian and PT-symmetric dimers and trimers. In the linear case, this approach provides us a handle for semi-analytically computing the spectrum [this amounts to the solution of a polynomial equation]. In the nonlinear case, it enables the computation of the linearization spectrum around the stationary solutions. The calculations showcase the oscillatory instabilities that strongly nonlinear states typically manifest. (literal)
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