Article

# Quantum breathers in a nonlinear Klein Gordon lattice

Service de Recherches de Métallurgie Physique, CEA-Saclay/DEN/DMN 91191-Gif-sur-Yvette Cedex, France

Physica D Nonlinear Phenomena (Impact Factor: 1.67). 01/2006; DOI: 10.1016/j.physd.2005.12.019 Source: arXiv

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**ABSTRACT:**We have calculated the lowest energy quantized breather excitations of both the β and the α Fermi-Pasta-Ulam monoatomic lattices and the diatomic β lattice within the ladder approximation. While the classical breather excitations form continua, the quantized breather excitations form a discrete hierarchy labeled by a quantum number n. Although the number of phonons is not conserved, the breather excitations correspond to multiple bound states of phonons. The n=2 breather spectra are composed of resonances in the two-phonon continuum and of discrete branches of infinitely long-lived excitations. The nonlinear attributes of these excitations become more pronounced at elevated temperatures. The calculated n=2 breather and the resonance of the monoatomic β lattice hybridize and exchange identity at the zone boundary and are in reasonable agreement with the results of previous calculations using the number-conserving approximation. However, by contrast, the breather spectrum of the α monoatomic lattice couples resonantly with the single-phonon spectrum and cannot be calculated within a number-conserving approximation. Furthermore, we show that for sufficiently strong nonlinearity, the α lattice breathers can be observed directly through the single-phonon inelastic neutron-scattering spectrum. As the temperature is increased, the single-phonon dispersion relation for the α lattice becomes progressively softer as the lattice instability is approached. For the diatomic β lattice, it is found that there are three distinct branches of n=2 breather dispersion relations, which are associated with three distinct two-phonon continua. The two-phonon excitations form three distinct continua: One continuum corresponds to the motion of two independent acoustic phonons, another to the motion of two independent optic phonons, and the last continuum is formed by propagation of two phonons that are one of each character. Each breather dispersion relation is split off the top from of its associated continuum and remains within the forbidden gaps between the continua. The energy splittings from the top of the continua rapidly increase, and the dispersions rapidly decrease with the decreasing energy widths of the associated continua. This finding is in agreement with recent observations of sharp branches of nonlinear vibrational modes in NaI through inelastic neutron-scattering measurements. Furthermore, since the band widths of the various continua successively narrow as the magnitude of their characteristic excitation energies increase, the finding is also in agreement the theoretical prediction that breather excitations in discrete lattices should be localized in the classical limit.Physical Review E 01/2012; 85(1 Pt 1):011129. · 2.31 Impact Factor - [Show abstract] [Hide abstract]

**ABSTRACT:**The dynamics of repulsive bosons condensed in an optical lattice is effectively described by the Bose-Hubbard model. The classical limit of this model, reproduces the dynamics of Bose-Einstein condensates, in a periodic potential, and in the superfluid regime. Such dynamics is governed by a discrete nonlinear Schrödinger equation. Several papers, addressing the study of the discrete nonlinear Schrödinger dynamics, have predicted the spontaneous generation of (classical) breathers in coupled condensates. In the present contribute, we shall focus on localized solutions (quantum breathers) of the full Bose-Hubbard model. We will show that solutions exponentially localized in space and periodic in time exist also in absence of randomness. Thus, this kind of states, reproduce a novel quantum localization phenomenon due to the interplay between bounded energy spectrum and non-linearity. Keywordsbreathers–Bose-Einstein condensates–localized states–optical latticesCentral European Journal of Physics 01/2011; 9(5):1248-1254. · 0.91 Impact Factor - [Show abstract] [Hide abstract]

**ABSTRACT:**Nonlinear classical Hamiltonian lattices exhibit generic solutions - discrete breathers. They are time-periodic and (typically exponentially) localized in space. The lattices have discrete translational symmetry. Discrete breathers are not confined to certain lattice dimensions. We will introduce the concept of these localized excitations and review their basic properties including dynamical and structural stability. We then focus on advances in the theory of discrete breathers in three directions - scattering of waves by these excitations, persistence of discrete breathers in long transient processes and thermal equilibrium, and their quantization. The second part of this review is devoted to a detailed discussion of recent experimental observations and studies of discrete breathers, including theoretical modelling of these experimental situations on the basis of the general theory of discrete breathers. in particular we will focus on their detection in Josephson junction networks, arrays of coupled nonlinear optical waveguides, Bose-Einstein condensates loaded on optical lattices, antiferromagnetic layered structures, PtCl based single crystals and driven micromechanical cantilever arrays. (C) 2008 Elsevier B.V. All rights reserved.Physics Reports 10/2008; 467(1-3):1-116. · 22.93 Impact Factor

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