Charge and energy transport by Holstein solitons in anharmonic one-dimensional systems

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Abstract

© 2019 Elsevier Ltd We consider the problem of electron transport and energy transfer in a one-dimensional molecular chain with non-dipole optical phonon mode. We take into account the dispersion of optical phonons, anharmonicity of the lattice on-site potential and electron-lattice interaction. In the lowest order linear approximation such a system admits solutions in the form of the Holstein polaron. Here, within the traveling wave formalism for the corresponding non-linear equations of motion in the long-wave limit, we show the existence of three particular types of exact analytical localized solutions. Two of them, here referred to as Holstein solitons of the first and second kind, respectively, describe a one-hump localized electron wave functions, while the third one displays two humps in the envelope of the wave function. We use the variational approach to reproduce the exact analytical profiles in the three cases of the particular normalized solutions and to variationally predict the existence of branches of normalized solutions for the three types of profiles. We confirm our findings by numerically continuing, in the parameter of velocity of propagation, the analytically exact particular solutions.
Original languageAmerican English
Pages (from-to)343-354
Number of pages307
JournalChaos, Solitons and Fractals
DOIs
StatePublished - 1 Feb 2019

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Charge Transport
Energy Transport
One-dimensional System
Solitons
solitary waves
Wave Function
Wave functions
Electron
Polaron
Phonons
Electron Transport
Particular Solution
Variational Approach
wave functions
Linear Approximation
Energy Transfer
Phonon
Traveling Wave
Envelope
electrons

Cite this

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abstract = "{\circledC} 2019 Elsevier Ltd We consider the problem of electron transport and energy transfer in a one-dimensional molecular chain with non-dipole optical phonon mode. We take into account the dispersion of optical phonons, anharmonicity of the lattice on-site potential and electron-lattice interaction. In the lowest order linear approximation such a system admits solutions in the form of the Holstein polaron. Here, within the traveling wave formalism for the corresponding non-linear equations of motion in the long-wave limit, we show the existence of three particular types of exact analytical localized solutions. Two of them, here referred to as Holstein solitons of the first and second kind, respectively, describe a one-hump localized electron wave functions, while the third one displays two humps in the envelope of the wave function. We use the variational approach to reproduce the exact analytical profiles in the three cases of the particular normalized solutions and to variationally predict the existence of branches of normalized solutions for the three types of profiles. We confirm our findings by numerically continuing, in the parameter of velocity of propagation, the analytically exact particular solutions.",
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Charge and energy transport by Holstein solitons in anharmonic one-dimensional systems. / Cisneros-Ake, Luis A.; Brizhik, L.

In: Chaos, Solitons and Fractals, 01.02.2019, p. 343-354.

Research output: Contribution to journalArticle

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AU - Brizhik, L.

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N2 - © 2019 Elsevier Ltd We consider the problem of electron transport and energy transfer in a one-dimensional molecular chain with non-dipole optical phonon mode. We take into account the dispersion of optical phonons, anharmonicity of the lattice on-site potential and electron-lattice interaction. In the lowest order linear approximation such a system admits solutions in the form of the Holstein polaron. Here, within the traveling wave formalism for the corresponding non-linear equations of motion in the long-wave limit, we show the existence of three particular types of exact analytical localized solutions. Two of them, here referred to as Holstein solitons of the first and second kind, respectively, describe a one-hump localized electron wave functions, while the third one displays two humps in the envelope of the wave function. We use the variational approach to reproduce the exact analytical profiles in the three cases of the particular normalized solutions and to variationally predict the existence of branches of normalized solutions for the three types of profiles. We confirm our findings by numerically continuing, in the parameter of velocity of propagation, the analytically exact particular solutions.

AB - © 2019 Elsevier Ltd We consider the problem of electron transport and energy transfer in a one-dimensional molecular chain with non-dipole optical phonon mode. We take into account the dispersion of optical phonons, anharmonicity of the lattice on-site potential and electron-lattice interaction. In the lowest order linear approximation such a system admits solutions in the form of the Holstein polaron. Here, within the traveling wave formalism for the corresponding non-linear equations of motion in the long-wave limit, we show the existence of three particular types of exact analytical localized solutions. Two of them, here referred to as Holstein solitons of the first and second kind, respectively, describe a one-hump localized electron wave functions, while the third one displays two humps in the envelope of the wave function. We use the variational approach to reproduce the exact analytical profiles in the three cases of the particular normalized solutions and to variationally predict the existence of branches of normalized solutions for the three types of profiles. We confirm our findings by numerically continuing, in the parameter of velocity of propagation, the analytically exact particular solutions.

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