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Asymmetric wave propagation through nonlinear PT-symmetric oligomers (Articolo in rivista)

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Asymmetric wave propagation through nonlinear PT-symmetric oligomers (Articolo in rivista) (literal)

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Jennie D'Ambroise (1); Panayotis G. Kevrekidis (2); Stefano Lepri (3) (2012)
Asymmetric wave propagation through nonlinear PT-symmetric oligomers
in Journal of physics. A, Mathematical and theoretical (Print); IOP Publishing Ltd., Bristol BS1 6BE (Regno Unito)
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1 Department of Mathematics, Bard College, Annandale-on-Hudson, NY 12504, United States 2 Department of Mathematics and Statistics, University of Massachusetts, Amherst, MA 01003-4515, United States 3 CNR-Consiglio Nazionale Delle Ricerche, Istituto Dei Sistemi Complessi, via Madonna del piano 10, I-50019 Sesto Fiorentino, Italy (literal)

Titolo

Abstract

In the present paper, we consider nonlinear PT-symmetric dimers and trimers (more generally, oligomers) embedded within a linear Schrödinger lattice. We examine the stationary states of such chains in the form of plane waves, and analytically compute their reflection and transmission coefficients through the nonlinear PT symmetric oligomer, as well as the corresponding rectification factors which clearly illustrate the asymmetry between left and right propagation in such systems. We examine not only the existence but also the dynamical stability of the plane wave states and interestingly find them to be unstable except in the vicinity of the linear limit. Lastly, we generalize our numerical considerations to the more physically relevant case of Gaussian initial wavepackets and confirm that the asymmetry in the transmission properties persists in the case of such wavepackets, as well. The role of potential asymmetries in the nonlinearity or in the gain/loss pattern is also considered. This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical devoted to Quantum physics with non-Hermitian operators. (literal)

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