Decay of a nonlinear impurity in a structured continuum from a nonlinear FanoAnderson model
Abstract
The decay dynamics of a nonlinear impurity mode embedded in a linear structured continuum is theoretically investigated in the framework of a nonlinear FanoAnderson model. A gradient flow dynamics for the survival probability is derived in the Van Hove ({lambda}{sup 2}t) limit by a multiplescale asymptotic analysis, and the role of nonlinearity on the decay law is discussed. In particular, it is shown that the existence of bound states embedded in the continuum acts as transient trapping states which slow down the decay. The dynamical behavior predicted in the {lambda}{sup 2}t limit is studied in detail for a simple tightbinding onedimensional lattice model, which may describe electron or photon transport in condensed matter or photonic systems. Numerical simulations of the underlying equations confirm, in particular, the trapping effect in the decay process due to bound states embedded in the continuum.
 Authors:
 Dipartimento di Fisica and Istituto di Fotonica e Nanotecnologie del CNR, Politecnico di Milano, Piazza Leonardo da Vinci 32, I20133 Milan (Italy)
 Publication Date:
 OSTI Identifier:
 20951414
 Resource Type:
 Journal Article
 Resource Relation:
 Journal Name: Physical Review. B, Condensed Matter and Materials Physics; Journal Volume: 75; Journal Issue: 18; Other Information: DOI: 10.1103/PhysRevB.75.184306; (c) 2007 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; BOUND STATE; DECAY; FLOW MODELS; IMPURITIES; INTERFERENCE; NONLINEAR PROBLEMS; ONEDIMENSIONAL CALCULATIONS; PHOTON TRANSPORT; SIMULATION; TRANSIENTS; TRANSPORT THEORY; TRAPPING
Citation Formats
Longhi, Stefano. Decay of a nonlinear impurity in a structured continuum from a nonlinear FanoAnderson model. United States: N. p., 2007.
Web. doi:10.1103/PHYSREVB.75.184306.
Longhi, Stefano. Decay of a nonlinear impurity in a structured continuum from a nonlinear FanoAnderson model. United States. doi:10.1103/PHYSREVB.75.184306.
Longhi, Stefano. Tue .
"Decay of a nonlinear impurity in a structured continuum from a nonlinear FanoAnderson model". United States.
doi:10.1103/PHYSREVB.75.184306.
@article{osti_20951414,
title = {Decay of a nonlinear impurity in a structured continuum from a nonlinear FanoAnderson model},
author = {Longhi, Stefano},
abstractNote = {The decay dynamics of a nonlinear impurity mode embedded in a linear structured continuum is theoretically investigated in the framework of a nonlinear FanoAnderson model. A gradient flow dynamics for the survival probability is derived in the Van Hove ({lambda}{sup 2}t) limit by a multiplescale asymptotic analysis, and the role of nonlinearity on the decay law is discussed. In particular, it is shown that the existence of bound states embedded in the continuum acts as transient trapping states which slow down the decay. The dynamical behavior predicted in the {lambda}{sup 2}t limit is studied in detail for a simple tightbinding onedimensional lattice model, which may describe electron or photon transport in condensed matter or photonic systems. Numerical simulations of the underlying equations confirm, in particular, the trapping effect in the decay process due to bound states embedded in the continuum.},
doi = {10.1103/PHYSREVB.75.184306},
journal = {Physical Review. B, Condensed Matter and Materials Physics},
number = 18,
volume = 75,
place = {United States},
year = {Tue May 01 00:00:00 EDT 2007},
month = {Tue May 01 00:00:00 EDT 2007}
}

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