Coherence and chaos in the driven, damped sine-Gordon chain

Bennett, Deborah; Bishop, A. R.; Trullinger, S. E.

doi:10.1007/bf01318320

Cited by 33 publications

(5 citation statements)

References 8 publications

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“…The narrow band noise spectrum consists of a few or a single [196] fundamental harmonics and their subharmonies [151,152]. There have been some proposals that the phenomena may be attributed to a chaotic motion of the CDW condensate [197][198][199][200]. Since, however, the fundamental frequency no ofnarrow band noise obeys Equation (5.13) weil, as already mentioned [151], it is now thought that the narrow band noise is tightly connected to a uniform motion of a whole CDW (or a soliton lattice).…”

Section: Noise Associated With the Non-ohmic Conductivitymentioning

confidence: 98%

Dynamical Properties of Quasi-One-Dimensional Conductors: A Phase Hamiltonian Approach

Fukuyama

Takayama

1985

Electronic Properties of Inorganic Quasi-One-Dimensional Compounds

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Section: Noise Associated With the Non-ohmic Conductivitymentioning

confidence: 98%

Dynamical Properties of Quasi-One-Dimensional Conductors: A Phase Hamiltonian Approach

Fukuyama

Takayama

1985

Electronic Properties of Inorganic Quasi-One-Dimensional Compounds

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“…Following other workers (Bennett et al 1982;Bishop et al 1983) we compute the dynamical structure factor for the displacement fields in our chain as the squared modulus of the Fourier transform of the dynamical variable…”

Section: Dynamical Structure Factormentioning

confidence: 99%

Dynamics of a Nonlinear Diatomic Chain. III. A Molecular Dynamics Study

Henry¹,

Oitmaa²

1985

Aust. J. Phys.

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We investigate the dynamics and the statistical mechanics of a nonlinear diatomic model for a solid which may undergo a displacive structural phase transition (DSPT), using the molecular dynamics (MD) technique. Snapshots of the lattice displacement pattern reveal the presence of kinks at low temperatures. MD collision experiments show that the kinks exhibit soliton-like behaviour. Phonon wave packets are observed to pass through kinks and kinks and anti-kinks interact with one another with little distortion. The MD data are used to calculate the dynamical structure factor for the displacement fields in the diatomic chain. The dynamical structure factor is found to exhibit a central peak when the lattice displacement pattern is dominated by kinks. At small but finite wave vectors the central peak splits producing a new excitation branch in addition to the usual soft-mode phonon side-band. The central peak does not arise from self-consistent phonons but is dependent on the presence of kinks. The height of the peak increases and the width of the peak decreases as the temperature goes to zero.

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“…In this way, to first order in F, the kink velocity may be calculated 19 by substituting into (12) instead of (p K the wave function (j> K 0 (x) of the static kink interpolating between the degenerate vacua.# lt 2° = lim F _» o 0 lt2 of the free chain, i.e., (13) Therefore, if F-» 0, the Landauer formula (13) implies that the rate coefficient o? 0 in (11) is proportional to F, i.e., a 0 vanishes for F=0.…”

Section: Eugen Magyarimentioning

confidence: 99%

“…(2) is unfortunately not available in closed analytic form. In the weak-field limit, however, the terminal velocity may be obtained immediately from the Landauer formula (13), which yields v = (ir/4ri)(k] 2 / F 0 ) I/2 JP, and thus the rate coefficient a 0 in the inertia mode (11), to first order in F, becomes a 0 = (Tr/4)(kl 2 …”

Section: = Af[rf*~ (>«?')*Dx]~\mentioning

confidence: 99%

Universal Localized Relaxation Mode of Uniformly Driven Kinks in Damped Multistable Systems

Magyari¹

1984

Phys. Rev. Lett.

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Linear arrays of damped multistable systems in a constant driving field F are considered in the continuum limit. The existence of a universal localized relaxation mode ("inertia mode") of the driven kinks is explicitly proven. This mode, of frequency OJ = -ir)/m 9 collapses in the undamped (77 -0) free (F-+0) chain into the Goldstone mode of the corresponding "free kink," and in a chain without inertia (m -*0) it relaxes instantaneously.PACS numbers: 63.20.Pw Linear arrays of uniformly 1 " 10 or periodically 11 " 15 driven and linearly damped multistable systems (mainly modeled by the sine-Gordon or 4 potential) have attracted in recent years increased attention. As a result of the interplay and competition between nonlinearity, damping, and driving force, fascinating effects can occur. 1 " 15 My aim in the present paper is to describe a new interesting phenomenon of this kind, which consists of the occurrence of a universal, localized, smooth relaxation mode of the uniformly driven kinks (domain walls) in linearly damped and tightly coupled multistable lattice-dynamical and similar systems. As mentioned in the Abstract, the existence of this universal relaxation mode is intrinsically connected to the inertia of the damped multistable chain. On this ground, it will be referred to hereafter in this paper as the "inertia mode" of the driven kinks.Let us consider therefore a linear chain of particles subjected to a constant external force F and described by the classical HamiltonianHere m is the particle mass, <$> { (t) represents the displacement of the i th particle at the time t from the site x { of a reference lattice, 0 f =B(p./dt 9 k is the strength of the harmonic coupling between neighboring particles, and V( { ) is a general "multistable" on-site potential. We assume that the chain deformation changes gradually from one lattice site to the next (tightly coupled particles), so that the continuum theory applies. We also assume that each particle is subjected to a damping force proportional to its velocity. In this way we obtain the following equation of motion for the displacement field n° correspond to degenerate minima 16 of the potential V(

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Coherence and chaos in the driven, damped sine-Gordon chain

Cited by 33 publications

References 8 publications

Dynamical Properties of Quasi-One-Dimensional Conductors: A Phase Hamiltonian Approach

Dynamical Properties of Quasi-One-Dimensional Conductors: A Phase Hamiltonian Approach

Dynamics of a Nonlinear Diatomic Chain. III. A Molecular Dynamics Study

Universal Localized Relaxation Mode of Uniformly Driven Kinks in Damped Multistable Systems

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