Long-range effects on superdiffusive algebraic solitons in anharmonic
chains |
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Authors: | C Brunhuber F G Mertens Y Gaididei |
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Institution: | 1.Physikalisches Institut, Universit?t Bayreuth,Bayreuth,Germany;2.Bogolyubov Institute for Theoretical Physics,Kiev,Ukraine |
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Abstract: | Studies on thermal diffusion of lattice solitons in Fermi-Pasta-Ulam (FPU)-like lattices
were recently generalized to the
case of dispersive long-range interactions (LRI) of the Kac-Baker form.
The variance of the soliton position shows a stronger than linear
time-dependence (superdiffusion) as found earlier for lattice solitons on FPU chains with
nearest-neighbour interactions (NNI). Since the superdiffusion seems to be generic for nontopological solitons, we want to
illuminate the role of the soliton shape on the superdiffusive mechanism.
Therefore, we concentrate on an FPU-like lattice with a certain class of power-law long-range interactions where the solitons
have algebraic tails instead of
the exponential tails in the case of FPU-type interactions (with or without Kac-Baker LRI).Despite of structurally similar
Langevin equations which hold for the soliton position and width of the two soliton types, the
algebraic solitons reach the superdiffusive long-time limit with a
characteristic t3/2 time-dependence much faster than
exponential solitons. The soliton shape determines the diffusion constant in the long-time limit that is approximately a factor
of π smaller for algebraic
solitons. Our results appear to be generic for nonlinear excitaitons in
FPU-chains, because the same superdiffusive time-dependence was also observed in
simulations with discrete breathers. |
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Keywords: | PACS" target="_blank">PACS 05 10 Gg Stochastic analysis methods (Fokker-Planck Langevin etc ) 05 45 Yv Solitons 05 40 -a Fluctuation phenomena random processes noise and Brownian motion 05 50 +q Lattice theory and statistics (Ising Potts etc ) |
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