Ratchet behavior in nonlinear Klein-Gordon systems with pointlike inhomogeneities

Morales-Molina, Luis; Mertens, Franz G.; Sánchez, Ángel

doi:10.1103/physreve.72.016612

Cited by 25 publications

(25 citation statements)

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“…[1][2][3][4][5][6][7] Generally speaking, the appearance of ratchetlike behavior requires two ingredients, departure from thermal equilibrium, either by using correlated stochastic forces or deterministic forces, and breaking of spatial and/or temporal symmetries. 4,6,[8][9][10][11][12][13][14] Many applications of the ratchet theoretical framework deal with the scenario of spatial symmetry breaking, beginning with the proposal for nonequilibrium rectifiers in Ref. 1.…”

Section: Introductionmentioning

confidence: 99%

Soliton ratchets in homogeneous nonlinear Klein-Gordon systems

Morales-Molina

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Sánchez

et al. 2006

Chaos: An Interdisciplinary Journal of Nonlinear Science

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We study in detail the ratchetlike dynamics of topological solitons in homogeneous nonlinear Klein-Gordon systems driven by a biharmonic force. By using a collective coordinate approach with two degrees of freedom, namely the center of the soliton, X͑t͒, and its width, l͑t͒, we show, first, that energy is inhomogeneously pumped into the system, generating as result a directed motion; and, second, that the breaking of the time shift symmetry gives rise to a resonance mechanism that takes place whenever the width l͑t͒ oscillates with at least one frequency of the external ac force. In addition, we show that for the appearance of soliton ratchets, it is also necessary to break the time-reversal symmetry. We analyze in detail the effects of dissipation in the system, calculating the average velocity of the soliton as a function of the ac force and the damping. We find current reversal phenomena depending on the parameter choice and discuss the important role played by the phases of the ac force. Our analytical calculations are confirmed by numerical simulations of the full partial differential equations of the sine-Gordon and 4 systems, which are seen to exhibit the same qualitative behavior. Ratchet, or rectification, phenomena in nonlinear nonequilibrium systems are receiving a great deal of attention in the past few years. A typical example of a ratchet occurs when pointlike particles are driven by deterministic or nonwhite stochastic forces. Under certain conditions related to the breaking of symmetries, unidirectional motion can take place although the applied force has zero average in time. The broken symmetries can be spatial, by introducing an asymmetric potential, or temporal, by using asymmetric periodic forces. This effect has found many applications in the design of devices for rectification or separation of different particles. Recently, ratchet dynamics is being studied in the context of solitons, trying to understand whether the fact that solitons, or nonlinear coherent excitations in general, are extended objects, allows for similar rectification phenomena. In nonlinear Klein-Gordon systems, it has been shown that ratchetlike behavior can be observed when driven by asymmetric periodic forces. However, the phenomenon is different from that seen in pointlike particles as the deformations of the soliton play a crucial role. In this paper we describe in detail these phenomena, analyze the mathematical conditions for its existence, explain the underlying mechanism originating the net motion, and study the highly nontrivial effects of dissipation on the motion. Our results may be related to recent observations of rectification in Josephson junctions and optical lattices.

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Section: Introductionmentioning

confidence: 99%

Soliton ratchets in homogeneous nonlinear Klein-Gordon systems

Morales-Molina

Quintero

Sánchez

et al. 2006

Chaos: An Interdisciplinary Journal of Nonlinear Science

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“…V). This is interesting because there are only a few reports on ratchets with nontopological solitons [12][13][14]; most of the literature concerns ratchets with topological solitons, e.g., [15][16][17][18][19]. In Ref.…”

Section: U + δU = R[u(xt); Xt]mentioning

confidence: 99%

Refined empirical stability criterion for nonlinear Schrödinger solitons under spatiotemporal forcing

et al. 2011

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We investigate the dynamics of traveling oscillating solitons of the cubic nonlinear Schrödinger (NLS) equation under an external spatiotemporal forcing of the form f (x,t) = a exp[iK(t)x]. For the case of time-independent forcing, a stability criterion for these solitons, which is based on a collective coordinate theory, was recently conjectured. We show that the proposed criterion has a limited applicability and present a refined criterion which is generally applicable, as confirmed by direct simulations. This includes more general situations where K(t) is harmonic or biharmonic, with or without a damping term in the NLS equation. The refined criterion states that the soliton will be unstable if the "stability curve" p(v), where p(t) and v(t) are the normalized momentum and the velocity of the soliton, has a section with a negative slope. In the case of a constant K and zero damping, we use the collective coordinate solutions to compute a "phase portrait" of the soliton where its dynamics is represented by two-dimensional projections of its trajectories in the four-dimensional space of collective coordinates. We conjecture, and confirm by simulations, that the soliton is unstable if a section of the resulting closed curve on the portrait has a negative sense of rotation.

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“…(1). In this case, according to [8,9] we have a directed motion whose direction is determined by the position of the inhomogeneities, and the dynamics reduces to a system very much like a rocking ratchet for a single particle [10]. Our results are shown in Fig.…”

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confidence: 83%

Inhomogeneous soliton ratchets under two ac forces

2006

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We extend our previous work on soliton ratchet devices ͓L. Morales-Molina et al., Eur. Phys. J. B 37, 79 ͑2004͔͒ to consider the joint effect of two ac forces including nonharmonic drivings, as proposed for particle ratchets by Savele'v et al. ͓Europhys. Lett. 67, 179 ͑2004͒; Phys. Rev. E 70, 066109 ͑2004͔͒. Current reversals due to the interplay between the phases, frequencies, and amplitudes of the harmonics are obtained. An analysis of the effect of the damping coefficient on the dynamics is presented. We show that solitons give rise to nontrivial differences in the phenomenology reported for particle systems that arise from their extended character. A comparison with soliton ratchets in homogeneous systems with biharmonic forces is also presented. This ratchet device may be an ideal candidate for Josephson junction ratchets with intrinsic large damping. The understanding of ratchet mechanisms is a very active field of wide interest by its potential application in the design of devices with new transport properties. The key feature of ratchet devices is their ability to rectify the motion of particles subjected to an external ac force with zero time average. Originally proposed as a toy model for molecular motors, in the last decade many proposals have been put forward for devices that use this ratchet phenomenon in different applications ͓1͔. Ratchets working with extended particles ͑solitons͒ were subsequently studied as a generalization of particle ratchets ͓2͔. Recently, an overdamped ratchet device for a single particle driven by two ac forces was introduced by Savele'v and coworkers ͓3͔, in which the combination of the two drivings produced a variety of interesting phenomena and allowed a finely tunable control. In view of the rich behavior demonstrated by this system, a very natural issue is its extension to soliton ratchets that have important applications which can benefit from this proposal.Soliton ratchets under the presence of two ac forces have been extensively studied ͓4,5͔ in homogeneous systems, i.e., without an underlying ratchet potential. In this case, it has been shown that the ratchet mechanism works only for asymmetric biharmonic forces, where the appearance of a directed translational motion is a result of the effective coupling between the internal mode ͑oscillations of the soliton width͒ and the external driving force. In this paper, we focus on a soliton ratchet device recently studied by us ͓7,8͔, based on a nonlinear Klein-Gordon model with a lattice of deltalike inhomogeneities that induce a ratchet potential for the solitons. As we will see, one of the advantages of our model as compared to the homogeneous system is that it works irrespectively of the symmetry of the ac driving: Directional transport takes place for ac forces with commensurate frequencies. Moreover, in the homogeneous system the motion drastically decreases for increasing damping, due to the slowing down of the soliton width oscillations ͓5͔, while in the present system the ratchet phenomenon is present up to rat...

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Ratchet behavior in nonlinear Klein-Gordon systems with pointlike inhomogeneities

Cited by 25 publications

References 69 publications

Soliton ratchets in homogeneous nonlinear Klein-Gordon systems

Soliton ratchets in homogeneous nonlinear Klein-Gordon systems

Refined empirical stability criterion for nonlinear Schrödinger solitons under spatiotemporal forcing

Inhomogeneous soliton ratchets under two ac forces

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