Controlling directed transport of matter-wave solitons using the ratchet effect

Rietmann, M.; Carretero-González, R.; Chacón, Ricardo

doi:10.1103/physreva.83.053617

Cited by 34 publications

(30 citation statements)

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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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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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“…This universal waveform is a direct consequence of the degree of symmetry breaking (DSB) mechanism: It is possible to consider a quantitative measure of the DSB on which the strength of directed transport by symmetry breaking must depend. Such a theory of the ratchet universality has been applied to predict successfully the behavior of two kinds of soliton ratchets [5,6]. The theory demonstrated in our original article [2] uses, among other theoretical ideas, ratchet universality to explain the interplay between thermal noise and symmetry breaking in the ratchet transport of Eq.…”

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confidence: 99%

Reply to “Comment on ‘Ratchet universality in the presence of thermal noise’ ”

Martínez

Chacón

2013

Phys. Rev. E

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The Comment by Quintero et al. does not dispute the central result of our paper [Phys. Rev. E 87, 062114 (2013)] which is a theory explaining the interplay between thermal noise and symmetry breaking in the ratchet transport of a Brownian particle moving on a periodic substrate subjected to a temporal biharmonic excitation γ [η sin (ωt) + α (1 − η) sin (2ωt + ϕ)]. In the Comment, the authors claim, on the sole basis of their numerical simulations for the particular case α = 2, that "there is no such universal force waveform and that the evidence obtained by the authors otherwise is due to their particular choice of parameters." Here we demonstrate by means of theoretical arguments and additional numerical simulations that all the conclusions of our original article are preserved. The foregoing Comment by Quintero et al.[1] offers some criticisms on certain particular (numerical) aspects of our previous paper [2], in which we studied theoretically and numerically a universal model -a Brownian particle moving on a periodic substrate subjected to a biharmonic excitation,where γ is an amplitude factor, and the parameters (η ∈ [0, 1] , α > 0) and ϕ account for the relative amplitude and initial phase difference of the two harmonics, respectively, while ξ (t) is a Gaussian white noise with zero mean and ξ (t) ξ (t + s) = δ (s), and σ = 2k b T with k b

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“…Relatively recently ratchet dynamics has been shown to exist for quasiparticles, such as solitons and large polarons [6][7][8][9][20][21][22][23]. In particular, it has been demonstrated that directed transport of bright solitons formed in a quasi-one-dimensional nondissipative Bose-Einstein condensate can be induced by a weak spatiotemporal biharmonic optical lattice potential [24][25][26][27].…”

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confidence: 99%

Thermal enhancement and stochastic resonance of polaron ratchets

et al. 2014

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. (2014) 'Thermal enhancement and stochastic resonance of polaron ratchet.', Physical review E., 89 (6). 062905.Further information on publisher's website:http://dx.doi.org/10.1103/PhysRevE.89.062905Publisher's copyright statement:Reprinted with permission from the American Physical Society: L. S. Brizhik, A. A. Eremko, B. M. A. G. Piette, and W. J. Zakrzewski, Physical Review E, 89, 062905, 2014. c 2014 by the American Physical Society. Readers may view, browse, and/or download material for temporary copying purposes only, provided these uses are for noncommercial personal purposes. Except as provided by law, this material may not be further reproduced, distributed, transmitted, modied, adapted, performed, displayed, published, or sold in whole or part, without prior written permission from the American Physical Society. Use policyThe full-text may be used and/or reproduced, and given to third parties in any format or medium, without prior permission or charge, for personal research or study, educational, or not-for-prot purposes provided that:• a full bibliographic reference is made to the original source • a link is made to the metadata record in DRO • the full-text is not changed in any way The full-text must not be sold in any format or medium without the formal permission of the copyright holders.Please consult the full DRO policy for further details. We study the ratchet drift of large polarons (solitons) in molecular diatomic chains induced by unbiased time periodic electric fields at nonzero temperature below its critical value. We show that, at a nonzero temperature, the critical value of the intensity of the electric field above which the ratchet phenomenon takes place is lower than at zero temperature for the same frequency of the field. We show that there is a range of temperatures for which the polaron drift is larger than that at zero temperature. We also show that temperature decreases the value of the lowest critical period of the field. And, finally, we demonstrate that there is a stochastic resonance in a polaron ratchet, namely that there is an optimal temperature at which the polaron drift is a maximum. The values of the stochastic resonance temperature, the lowest critical values of the field intensity, and its period depend on various parameters of the system and, in particular, on the anisotropy of the chain parameters. This temperature induced decrease of the critical value of the field intensity and its period, as well as the stochastic resonance itself, may be important for practical applications of the ratchet phenomenon in systems involving conducting polymers and other low-dimensional materials. They may also be important in some biological macromolecules where the ratchet phenomenon could take place in biomotors and energy and/or charge transport.

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Controlling directed transport of matter-wave solitons using the ratchet effect

Cited by 34 publications

References 38 publications

Refined empirical stability criterion for nonlinear Schrödinger solitons under spatiotemporal forcing

Refined empirical stability criterion for nonlinear Schrödinger solitons under spatiotemporal forcing

Reply to “Comment on ‘Ratchet universality in the presence of thermal noise’ ”

Thermal enhancement and stochastic resonance of polaron ratchets

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