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J Cuevas, C Katerji, B Sánchez-Rey and A Álvarez Non Linear Physics Group of the University of Seville Department of Applied Physics I February 21st, 2003 Influence of moving breathers on vacancies migration

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Previous: Experimental evidence Model Vacancy MB & vacancy Results Outline

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X X X X X radiation (Ag) Experimental evidence: defects migrate sample (Si) X X X X X XX X X X XX X X X layer (Ni) 1 2 4 3

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01234 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Morse potentials x W(x) -0.500.511.522.533.5 0 0.01 0.02 0.03 0.04 0.05 0.06 sine-Gordon potential x V(x) The model Frenkel-Kontorova + anharmonic interaction

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Plane waves (phonons) The Hamiltonian: The linearized equations: Dispersion relation Frecuency breather:,,

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The vacancy

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The moving breather Energy added to the breather:

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00.13 Gaussian distribution K Forinash, T Cretegny and M Peyrard. Local modes and localization in a multicomponent nonlinear lattices. Phys. Rev. E, 55:4740, 1997. Analysis: b (Morse potential) The moving breather

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Three types of phenomena i) The vacancy moves backwards. ii) The vacancy moves forwards. iii) The vacancy remains at its site.

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MB i) The most probably is that the vacancy moves backwards

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MB ii) But the vacancy can move forwards

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MB iii) And the vacancy can stay motion-less

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C=0.4 remains forwards backwards Probability Probability of the vacancy’s movement

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C=0.5 backwards forwards remains Probability Probability of the vacancy’s movement

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Morse potentials The coupling forces

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C=0.5 backwards forwards remains Probability Probability of the vacancy’s movement

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C=0.4 remains forwards backwards Probability Probability of the vacancy’s movement

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C=0.4 bifurcation

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C=0.5 bifurcation

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C=0.4 n x Amplitude maxima of a vacancy breather bifurcation

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C=0.5 n x Amplitude maxima of a vacancy breather bifurcation

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Conclusions The moving breathers can move vacancies. The behaviour is very complex and it depends of the values of the coupling. The changes of the probabilities of the different movements of the vacancies are related with the existence of bifurcations. Is there a more rich complexity from 1-dim to 2-dim ? Thank you very much.

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