Solitons in a nonlinear model of spin transport in helical molecules

Albares, Paz; Díaz, Elena; Cerveró, José M.; Domı́nguez-Adame, F.; Díez, E.; Estévez, P.G.

doi:10.1103/physreve.97.022210

Cited by 15 publications

(17 citation statements)

References 49 publications

(73 reference statements)

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“…The singular manifold method has been applied in [39] to this Lax pair in order to derive Darboux transformations and an iterative procedure that yields solitonic solutions for equation (21).…”

Section: Electron Spin Dynamics In a Deformable Helical Moleculementioning

confidence: 99%

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Spin dynamics in helical molecules with nonlinear interactions

et al. 2018

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It is widely admitted that the helical conformation of certain chiral molecules may induce a sizable spin selectivity observed in experiments. Spin selectivity arises as a result of the interplay between a helicity-induced spin-orbit coupling (SOC) and electric dipole fields in the molecule. From the theoretical point of view, different phenomena might affect the spin dynamics in helical molecules, such as quantum dephasing, dissipation and the role of metallic contacts. With a few exceptions, previous studies usually neglect the local deformation of the molecule about the carrier, but this assumption seems unrealistic to describe charge transport in molecular systems. We introduce an effective model describing the electron spin dynamics in a deformable helical molecule with weak SOC. We find that the electron-lattice interaction allows the formation of stable solitons such as bright solitons with well defined spin projection onto the molecule axis. We present a thorough study of these bright solitons and analyze their possible impact on the spin dynamics in deformable helical molecules.

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Section: Electron Spin Dynamics In a Deformable Helical Moleculementioning

confidence: 99%

“…where  H is given in equation (7a) and g>0 is a dimensionless constant. The integrability of this equation has been recently analyzed by using the Painlevé test [39] which requires that the components of c admit the Laurent expansion å c x…”

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confidence: 99%

Spin dynamics in helical molecules with nonlinear interactions

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“…A thorough study of the soliton solutions have been presented and discussed in Refs. [21,22]. In the following section we discuss how bright solitons, similarly to the wellknown Davydov's soliton [29], are affected when Eq.…”

Section: A Continuum Approximationmentioning

confidence: 99%

“…In addition, the local deformation of the molecule about the carrier gives rise to nonlinear effects that ultimately can lead to self-trapping [20]. Nevertheless, theoretical models have taken into account the effects of molecular deformation and nonlinear interactions only very recently [21][22][23][24].…”

Section: Introductionmentioning

confidence: 99%

Effective nonlinear model for electron transport in deformable helical molecules

et al. 2018

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The helical conformation of electric dipoles in some chiral molecules, such as DNA and bacteriorhodopsin, induces a spin-orbit coupling that results in a sizable spin selectivity of electrons. The local deformation of the molecule about the moving electron may affect the spin dynamics due to the appearance of bright solitons with well-defined spin projection onto the molecule axis. In this work, we introduce an effective model for electron transport in a deformable helical molecular lattice that resembles the nonlinear Kronig-Penney model in the adiabatic approximation. In addition, the continuum limit of our model is achieved when the dipole-dipole distance is smaller than the spatial extent of the bright soliton, as discussed by E. Díaz et al. [N. J. Phys. 20, 043055 (2018)]. In this limit, our model reduces to an extended Davydov model. Finally, we also focus on perturbations to the bright soliton that arise naturally in the context of real helical molecules. We conclude that the continuum approximation provides excellent results in more complex scenarios.

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“…A different problem is the determination of the integrability of a nonlinear partial differential equation, as well as the derivation of its Lax pair in the case of integrability. The Painlevé property and the singular manifold method derived from such property are extremely useful procedures in order to prove the integrability and to derive the Lax pair of an integrable system [9], [10], [11], [12]. This paper is devoted to the study of a multi-component nonlinear Schrödinger (NLS) Equation in 2 + 1 dimensions and its associated linear problem.…”

Section: Introductionmentioning

confidence: 99%

Spectral problem for a two-component nonlinear Schrödinger equation in 2+1 dimensions: Singular manifold method and Lie point symmetries

Albares

Conde

Estévez

2019

Applied Mathematics and Computation

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An integrable two-component nonlinear Schrödinger equation in 2 + 1 dimensions is presented. The singular manifold method is applied in order to obtain a three-component Lax pair. The Lie point symmetries of this Lax pair are calculated in terms of nine arbitrary functions and one arbitrary constant that yield a non-trivial infinite-dimensional Lie algebra. The main non-trivial similarity reductions associated to these symmetries are identified. The spectral parameter of the reduced spectral problem appears as a consequence of one of the symmetries.

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Solitons in a nonlinear model of spin transport in helical molecules

Cited by 15 publications

References 49 publications

Spin dynamics in helical molecules with nonlinear interactions

Spin dynamics in helical molecules with nonlinear interactions

Effective nonlinear model for electron transport in deformable helical molecules

Spectral problem for a two-component nonlinear Schrödinger equation in 2+1 dimensions: Singular manifold method and Lie point symmetries

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