### Abstract

An exact solution of a discrete nonlinear Schroumldinger equation, obtained recently for the site occupation probabilities in a two-site system such as a molecular dimer, has shown that the probabilities evolve in the form of Jacobian elliptic functions and exhibit a self-trapping transition. On the basis of that solution, we examine the effect of nonlinearities on the quasielastic scattering function in a dimer. The calculation is appropriate to the scattering of probe particles such as neutrons off moving quasiparticles which interact with lattice vibrations strongly enough to produce nonlinear effects while moving in the lattice. A well-known example is provided by hydrogen atoms diffusing among sites around impurities, e.g., oxygen, in metals such as niobium. Our calculation results in explicit expressions for the scattering spectrum. They exhibit the phenomenon of motional narrowing even in the absence of true damping. Comparison of the results for the undamped nonlinear dimer and the damped linear dimer uncover striking similarities as well as differences.

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

Pages (from-to) | 1473-1484 |

Number of pages | 12 |

Journal | Physical Review B |

Volume | 35 |

Issue number | 4 |

DOIs | |

Publication status | Published - 1987 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Condensed Matter Physics

### Cite this

*Physical Review B*,

*35*(4), 1473-1484. https://doi.org/10.1103/PhysRevB.35.1473

**Nonlinear effects in quasielastic neutron scattering : Exact line-shape calculation for a dimer.** / Kenkre, V. M.; Tsironis, G. P.

Research output: Contribution to journal › Article

*Physical Review B*, vol. 35, no. 4, pp. 1473-1484. https://doi.org/10.1103/PhysRevB.35.1473

}

TY - JOUR

T1 - Nonlinear effects in quasielastic neutron scattering

T2 - Exact line-shape calculation for a dimer

AU - Kenkre, V. M.

AU - Tsironis, G. P.

PY - 1987

Y1 - 1987

N2 - An exact solution of a discrete nonlinear Schroumldinger equation, obtained recently for the site occupation probabilities in a two-site system such as a molecular dimer, has shown that the probabilities evolve in the form of Jacobian elliptic functions and exhibit a self-trapping transition. On the basis of that solution, we examine the effect of nonlinearities on the quasielastic scattering function in a dimer. The calculation is appropriate to the scattering of probe particles such as neutrons off moving quasiparticles which interact with lattice vibrations strongly enough to produce nonlinear effects while moving in the lattice. A well-known example is provided by hydrogen atoms diffusing among sites around impurities, e.g., oxygen, in metals such as niobium. Our calculation results in explicit expressions for the scattering spectrum. They exhibit the phenomenon of motional narrowing even in the absence of true damping. Comparison of the results for the undamped nonlinear dimer and the damped linear dimer uncover striking similarities as well as differences.

AB - An exact solution of a discrete nonlinear Schroumldinger equation, obtained recently for the site occupation probabilities in a two-site system such as a molecular dimer, has shown that the probabilities evolve in the form of Jacobian elliptic functions and exhibit a self-trapping transition. On the basis of that solution, we examine the effect of nonlinearities on the quasielastic scattering function in a dimer. The calculation is appropriate to the scattering of probe particles such as neutrons off moving quasiparticles which interact with lattice vibrations strongly enough to produce nonlinear effects while moving in the lattice. A well-known example is provided by hydrogen atoms diffusing among sites around impurities, e.g., oxygen, in metals such as niobium. Our calculation results in explicit expressions for the scattering spectrum. They exhibit the phenomenon of motional narrowing even in the absence of true damping. Comparison of the results for the undamped nonlinear dimer and the damped linear dimer uncover striking similarities as well as differences.

UR - http://www.scopus.com/inward/record.url?scp=0001672469&partnerID=8YFLogxK

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U2 - 10.1103/PhysRevB.35.1473

DO - 10.1103/PhysRevB.35.1473

M3 - Article

VL - 35

SP - 1473

EP - 1484

JO - Physical Review B

JF - Physical Review B

SN - 1098-0121

IS - 4

ER -