# Decay of a nonlinear impurity in a structured continuum from a nonlinear Fano-Anderson 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 Fano-Anderson model. A gradient flow dynamics for the survival probability is derived in the Van Hove ({lambda}{sup 2}t) limit by a multiple-scale 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 tight-binding one-dimensional 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, I-20133 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; ONE-DIMENSIONAL CALCULATIONS; PHOTON TRANSPORT; SIMULATION; TRANSIENTS; TRANSPORT THEORY; TRAPPING

### Citation Formats

```
Longhi, Stefano.
```*Decay of a nonlinear impurity in a structured continuum from a nonlinear Fano-Anderson 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 Fano-Anderson model*. United States. doi:10.1103/PHYSREVB.75.184306.

```
Longhi, Stefano. Tue .
"Decay of a nonlinear impurity in a structured continuum from a nonlinear Fano-Anderson 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 Fano-Anderson 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 Fano-Anderson model. A gradient flow dynamics for the survival probability is derived in the Van Hove ({lambda}{sup 2}t) limit by a multiple-scale 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 tight-binding one-dimensional 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}

}