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Title: Ground-state properties of small-size nonlinear dynamical lattices

Abstract

We investigate the ground state of a system of interacting particles in small nonlinear lattices with M{>=}3 sites, using as a prototypical example the discrete nonlinear Schroedinger equation that has been recently used extensively in the contexts of nonlinear optics of waveguide arrays and Bose-Einstein condensates in optical lattices. We find that, in the presence of attractive interactions, the dynamical scenario relevant to the ground-state and the lowest-energy modes of such few-site nonlinear lattices reveals a variety of nontrivial features that are absent in the large/infinite lattice limits: the single-pulse solution and the uniform solution are found to coexist in a finite range of the lattice intersite coupling where, depending on the latter, one of them represents the ground state; in addition, the single-pulse mode does not even exist beyond a critical parametric threshold. Finally, the onset of the ground-state (modulational) instability appears to be intimately connected with a nonstandard (''double transcritical'') type of bifurcation that, to the best of our knowledge, has not been reported previously in other physical systems.

Authors:
;  [1];  [2];  [3]
  1. Dipartimento di Fisica, Politecnico di Torino, Corso Duca degli Abruzzi 24, I-10129 Torino (Italy)
  2. Department of Mathematics and Statistics, University of Massachusetts, Amherst Massachusetts 01003-4515 (United States)
  3. Dipartimento di Fisica and CNR-INFM, Universita degli Studi di Parma, Parco Area delle Scienze 7/a, I-43100 Parma (Italy)
Publication Date:
OSTI Identifier:
21072276
Resource Type:
Journal Article
Resource Relation:
Journal Name: Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics; Journal Volume: 75; Journal Issue: 1; Other Information: DOI: 10.1103/PhysRevE.75.016212; (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; BIFURCATION; BOSE-EINSTEIN CONDENSATION; COUPLING; GROUND STATES; INSTABILITY; LATTICE FIELD THEORY; MATHEMATICAL SOLUTIONS; NONLINEAR OPTICS; NONLINEAR PROBLEMS; PULSES; SCHROEDINGER EQUATION; WAVEGUIDES

Citation Formats

Buonsante, P., Penna, V., Kevrekidis, P. G., and Vezzani, A. Ground-state properties of small-size nonlinear dynamical lattices. United States: N. p., 2007. Web. doi:10.1103/PHYSREVE.75.016212.
Buonsante, P., Penna, V., Kevrekidis, P. G., & Vezzani, A. Ground-state properties of small-size nonlinear dynamical lattices. United States. doi:10.1103/PHYSREVE.75.016212.
Buonsante, P., Penna, V., Kevrekidis, P. G., and Vezzani, A. Mon . "Ground-state properties of small-size nonlinear dynamical lattices". United States. doi:10.1103/PHYSREVE.75.016212.
@article{osti_21072276,
title = {Ground-state properties of small-size nonlinear dynamical lattices},
author = {Buonsante, P. and Penna, V. and Kevrekidis, P. G. and Vezzani, A.},
abstractNote = {We investigate the ground state of a system of interacting particles in small nonlinear lattices with M{>=}3 sites, using as a prototypical example the discrete nonlinear Schroedinger equation that has been recently used extensively in the contexts of nonlinear optics of waveguide arrays and Bose-Einstein condensates in optical lattices. We find that, in the presence of attractive interactions, the dynamical scenario relevant to the ground-state and the lowest-energy modes of such few-site nonlinear lattices reveals a variety of nontrivial features that are absent in the large/infinite lattice limits: the single-pulse solution and the uniform solution are found to coexist in a finite range of the lattice intersite coupling where, depending on the latter, one of them represents the ground state; in addition, the single-pulse mode does not even exist beyond a critical parametric threshold. Finally, the onset of the ground-state (modulational) instability appears to be intimately connected with a nonstandard (''double transcritical'') type of bifurcation that, to the best of our knowledge, has not been reported previously in other physical systems.},
doi = {10.1103/PHYSREVE.75.016212},
journal = {Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics},
number = 1,
volume = 75,
place = {United States},
year = {Mon Jan 15 00:00:00 EST 2007},
month = {Mon Jan 15 00:00:00 EST 2007}
}