Computer simulations of intrinsic localized modes in 1-D anharmonic lattices

Burkalov, V.M.; Kiselev, S. A.; Pyrkov, V. N.

doi:10.1016/0038-1098(90)90496-x

Cited by 40 publications

(14 citation statements)

References 3 publications

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“…This is achieved using either Runge-Kutta methods or Verlet (leapfrog) algorithms [149]. The results are typically presented as some snapshots of the amplitude or energy distribution in the lattice during the actual integration [173], [36], [37], [38], [39], [122], [117], [35], [170], [174], [109], [108], [107], [106], [9], [7], [51], [110], [197]. The findings strongly suggest that there exist solutions of the lattice dynamics which appear to be similar to breather solutions.…”

Section: Numerical Evidencementioning

confidence: 99%

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: Numerical Evidencementioning

confidence: 99%

Discrete breathers

1998

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“…Indeed breather-like excitations have been observed in a variety of different models at finite temperatures [10]. For some special models with additional conservation laws semianalytical statements about the contribution of DBs to thermal equilibrium have been derived [11].…”

Section: Introductionmentioning

confidence: 99%

Discrete breathers in thermal equilibrium: distributions and energy gaps

Eleftheriou

Flach

2005

Physica D: Nonlinear Phenomena

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We study a discrete two-dimensional nonlinear system that allows for discrete breather solutions. We perform a spectral analysis of the lattice dynamics at thermal equilibrium and use a cooling technique to measure the amount of breathers at thermal equilibrium. Our results confirm the existence of an energy threshold for discrete breathers. The cooling method provides with a novel computational technique of measuring and analyzing discrete breather distribution properties in thermal equilibrium.

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“…When the diatomic lattices or the lattices with alternating interactions where the linear phonon spectra contains both acoustic modes and optical modes are taken into account, the situation may be quite different. The DBs properties studied in diatomic lattices [36][37][38][39][40][41][42][43][44][45][46] indeed support this difference, i.e., a new kind of DBs, the gap DBs with frequencies lying in the gap between acoustic modes and optical modes can emerge when the mass ratio is appropriate [46]. However, in spite of these studies, at present whether and, if yes, what roles the gap DBs would play in heat transport is still an open question.…”

Section: Discrete Breathersmentioning

confidence: 85%

“…5]. We recall that P (ω) for ω > 2 corresponds to the optical DBs [36,37] and P (ω) for ω in the gap between the acoustic and optical branches corresponds to the gap DBs [40] first.…”

Section: Discrete Breathersmentioning

confidence: 99%

Heat transport enhanced by optical phonons in one-dimensional anharmonic lattices with alternating bonds

2013

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In lattice systems, the effects of optical phonons on heat transport are usually neglected due to their relatively small group velocities compared with acoustic phonons, or even assumed to be negative because introducing optical phonons may simultaneously reduce the group velocities of acoustic phonons. In order to well understand the role played by optical phonons, we propose a one-dimensional anharmonic lattice model with alternating interactions, where the optical phonons can be conveniently tuned. We find that in contrast to previous studies, the optical phonons (in coordination with the nonlinearities) can enhance heat transport in the thermodynamical limit, suggesting that optical phonons can also play an active role. The underlying mechanism is related to the effects of two kinds of nonlinear excitations, i.e., the optical and the gap discrete breathers (DBs). These DBs release energy and in turn facilitate heat transport.

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Computer simulations of intrinsic localized modes in 1-D anharmonic lattices

Cited by 40 publications

References 3 publications

Discrete breathers

Discrete breathers

Discrete breathers in thermal equilibrium: distributions and energy gaps

Heat transport enhanced by optical phonons in one-dimensional anharmonic lattices with alternating bonds

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