### Abstract

We propose an analytical approach to study the one-dimensional acoustic polaron model that includes an on-site external potential applied to each chain molecule. The key to the approach is an exact discrete solution for the chain-deformation field given in terms of a (quasi)particle wave function. For this purpose we introduce a set of polynomial series that resemble the Chebyshev polynomials. We call these series the hyperbolic Chebyshev polynomials. Using next a properly chosen discrete trial function for the wave function envelope, we obtain simple expressions for the variational energy of the system. Contrary to an isolated (without any external potential) molecular chain, the polaron state (Davydov soliton) is shown to exist only for appropriate system parameters while the delocalized (exciton) state can always exist. As a result, the following three regimes can be specified for the chain with an on-site potential: (i) the polaron is a ground state and the exciton is a metastable state, (ii) the polaron is a metastable state and the exciton is a (delocalized) ground state, and (iii) the polaron state does not exist and only the exciton exists, being a ground state. Two characteristic dimensionless parameters are found in terms of which a criterion of existence of (stable and metastable) polaron states and their nonexistence is formulated. Finally, the Davydov soliton experiences depinning in a particular case of system parameters, resulting in a transparent regime of uniform propagation of the soliton with very small size.

Original language | English |
---|---|

Article number | 054302 |

Pages (from-to) | 054302-1 - 054302-14 |

Journal | Physical Review B: Condensed Matter and Materials Physics |

Volume | 63 |

Issue number | 5 |

DOIs | |

Publication status | Published - 2001 |

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*Physical Review B: Condensed Matter and Materials Physics*,

*63*(5), 054302-1 - 054302-14. [054302]. https://doi.org/10.1103/PhysRevB.63.054302

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*Physical Review B: Condensed Matter and Materials Physics*, vol. 63, no. 5, 054302, pp. 054302-1 - 054302-14. https://doi.org/10.1103/PhysRevB.63.054302

**Analytical approach to the Davydov-Scott theory with on-site potential.** / Zolotaryuk, Y.; Eilbeck, J. C.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Analytical approach to the Davydov-Scott theory with on-site potential

AU - Zolotaryuk, Y.

AU - Eilbeck, J. C.

PY - 2001

Y1 - 2001

N2 - We propose an analytical approach to study the one-dimensional acoustic polaron model that includes an on-site external potential applied to each chain molecule. The key to the approach is an exact discrete solution for the chain-deformation field given in terms of a (quasi)particle wave function. For this purpose we introduce a set of polynomial series that resemble the Chebyshev polynomials. We call these series the hyperbolic Chebyshev polynomials. Using next a properly chosen discrete trial function for the wave function envelope, we obtain simple expressions for the variational energy of the system. Contrary to an isolated (without any external potential) molecular chain, the polaron state (Davydov soliton) is shown to exist only for appropriate system parameters while the delocalized (exciton) state can always exist. As a result, the following three regimes can be specified for the chain with an on-site potential: (i) the polaron is a ground state and the exciton is a metastable state, (ii) the polaron is a metastable state and the exciton is a (delocalized) ground state, and (iii) the polaron state does not exist and only the exciton exists, being a ground state. Two characteristic dimensionless parameters are found in terms of which a criterion of existence of (stable and metastable) polaron states and their nonexistence is formulated. Finally, the Davydov soliton experiences depinning in a particular case of system parameters, resulting in a transparent regime of uniform propagation of the soliton with very small size.

AB - We propose an analytical approach to study the one-dimensional acoustic polaron model that includes an on-site external potential applied to each chain molecule. The key to the approach is an exact discrete solution for the chain-deformation field given in terms of a (quasi)particle wave function. For this purpose we introduce a set of polynomial series that resemble the Chebyshev polynomials. We call these series the hyperbolic Chebyshev polynomials. Using next a properly chosen discrete trial function for the wave function envelope, we obtain simple expressions for the variational energy of the system. Contrary to an isolated (without any external potential) molecular chain, the polaron state (Davydov soliton) is shown to exist only for appropriate system parameters while the delocalized (exciton) state can always exist. As a result, the following three regimes can be specified for the chain with an on-site potential: (i) the polaron is a ground state and the exciton is a metastable state, (ii) the polaron is a metastable state and the exciton is a (delocalized) ground state, and (iii) the polaron state does not exist and only the exciton exists, being a ground state. Two characteristic dimensionless parameters are found in terms of which a criterion of existence of (stable and metastable) polaron states and their nonexistence is formulated. Finally, the Davydov soliton experiences depinning in a particular case of system parameters, resulting in a transparent regime of uniform propagation of the soliton with very small size.

UR - http://www.scopus.com/inward/record.url?scp=0035133320&partnerID=8YFLogxK

U2 - 10.1103/PhysRevB.63.054302

DO - 10.1103/PhysRevB.63.054302

M3 - Article

VL - 63

SP - 054302-1 - 054302-14

JO - Physical Review B: Condensed Matter and Materials Physics

JF - Physical Review B: Condensed Matter and Materials Physics

SN - 1098-0121

IS - 5

M1 - 054302

ER -