Stability of intrinsic localized modes in anharmonic 1-D lattices

Chubykalo, O. A.; Kovalev, A. S.; Usatenko, O. V.

doi:10.1016/0375-9601(93)90739-m

Cited by 27 publications

(21 citation statements)

References 6 publications

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“…if these perturbations are linearly stable, then we obtain bound states which are not merely a consequence of the existence of the DB solution itself. Such eigenstates were observed in many numerical studies [157], [46], [52], [87], [90], [88], [84], and especially studied systematically by Marin and Aubry in [140].…”

Section: A Phonon Trappingmentioning

confidence: 95%

“…Indeed the Floquet matrix diagonalization yields both extended and localized eigenvectors. The existence of localized eigenvectors has been long suggested in the literature (stability/instability of even/odd parity modes [157], [46], XC/XN modes [51], [129]). In fact in many cases the spatial symmetries of DB solutions have been correlated with the dynamical linear stability.…”

Section: A Linear Stability Analysismentioning

confidence: 99%

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Discrete breathers

1998

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Nonlinear classical Hamiltonian lattices exhibit generic solutions in the form of discrete breathers. These solutions are time-periodic and (typically exponentially) localized in space. The lattices exhibit discrete translational symmetry. Discrete breathers are not confined to certain lattice dimensions. Necessary ingredients for their occurence are the existence of upper bounds on the phonon spectrum (of small fluctuations around the groundstate) of the system as well as the nonlinearity in the differential equations. We will present existence proofs, formulate necessary existence conditions, and discuss structural stability of discrete breathers. The following results will be also discussed: the creation of breathers through tangent bifurcation of band edge plane waves; dynamical stability; details of the spatial decay; numerical methods of obtaining breathers; interaction of breathers with phonons and electrons; movability; influence of the lattice dimension on discrete breather properties; quantum lattices -quantum breathers.Finally we will formulate a new conceptual aproach capable of predicting whether discrete breather exist for a given system or not, without actually solving for the breather. We discuss potential applications in lattice dynamics of solids (especially molecular crystals), selective bond excitations in large molecules, dynamical properties of coupled arrays of Josephson junctions, and localization of electromagnetic waves in photonic crystals with nonlinear response.

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Section: A Phonon Trappingmentioning

confidence: 95%

Section: A Linear Stability Analysismentioning

confidence: 99%

Discrete breathers

1998

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“…(22) or Eq. (23). For large T and a there is a competition between the terms in the expansion, with large T favoring states of lower energy and large a favoring states that drop off most slowly in their spatial coordinate, which in general will be of higher energy.…”

Section: Localizationmentioning

confidence: 99%

“…(2), gives rise to interesting patterns of behavior not seen in the selfcoupling case. There is first the phenomenon of moving breathers [20,21,22,23,24,25], which obviously will not occur when only one site and its neighbors are subject to nonlinearity. Movement can be suppressed by taking appropriate initial conditions (equal and opposite position displacements) so that the stationary breather consists of a pair of atoms oscillating with respect to each other.…”

Section: Effect Of Dropping Nonlinearity For "Non-breather" Atomsmentioning

confidence: 99%

Structure and time-dependence of quantum breathers

Schulman¹,

Tolkunov²,

Mihóková³

2006

Chemical Physics

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Quantum states of a discrete breather are studied in two ways. One method involves numerical diagonalization of the Hamiltonian, the other uses the path integral to examine correlations in the eigenstates. In both cases only the central nonlinearity is retained. To reduce truncation effects in the numerical diagonalization, a basis is used that involves a quadratic local mode. A similar device is used in the path integral method for deducing localization. Both approaches lead to the conclusion that aside from quantum tunneling the quantized discrete breather is stable.

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“…Earlier studies had to rely either on numerical simulation [14] or on excessive approximations [15]. With the new highaccuracy methods available, one can afford to perform the full analysis.…”

Section: Stability Analysis Of Stationary Breathersmentioning

confidence: 99%

Intrinsic localized modes: Discrete breathers. Existence and linear stability

Marín

Aubry

Floría

1998

Physica D: Nonlinear Phenomena

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We present some examples of detailed analysis of intrinsic localized modes in lattices, using the accurate numerical methods derived from the proof of existence of MacKay-Aubry. We report on some improvements on the methods, which are then used to the fullest to obtain the Floquet analysis of the breather solutions. Such calculations are possible taking into account the whole lattice, without any approximations. This yields an unprecedented detail of the mechanisms that govern instabilities in discrete breathers, giving a complete picture of the interplay between localized ("internal") and extended ("phonon-like") instabilities.

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Stability of intrinsic localized modes in anharmonic 1-D lattices

Cited by 27 publications

References 6 publications

Discrete breathers

Discrete breathers

Structure and time-dependence of quantum breathers

Intrinsic localized modes: Discrete breathers. Existence and linear stability

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