Serge Aubry - Physics Department . Technion

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$Turbulence-degraded wave fronts as fractal surfaces - Physics ...$

What is the long time behavior of an initially localized wavepacket 1-Does it spread to zero amplitude (diffusion)? 2- does it remain localized (absence of diffusion)? 3- Does a part of the energy spread and another part remains localized? The answer is known in linear systems Diffusion if the linear spectrum is continuous Absence of diffusion when the linear spectrum is purely discrete (for example in disordered systems with Anderson localization) Nonlinear systems? Serge Aubry, Aubry, LLB, FRANCE
I-Nonlinear spatially periodic systems: (with no disorder) Incomplete diffusion of a wavepacket Possible formation of Discrete Breathers (spatially localized time periodic solutions) Sievers and Takeno 1988 (ILM) Campbell and Peyrard 1990 (Discrete Breathers-DBs) Generic Nonlinear Excitations (non restricted to special integrable models) in 1D, 2D, 3D… periodic arrays of nonlinear oscillators Serge Aubry, Aubry, LLB, FRANCE
Page 1: Suppression of Energy Diffusion in
Page 5 and 6: Initial wavepacket Time periodic so
Page 7 and 8: II- Exact Time Periodic Solutions (
Page 9 and 10: Numerical Calculation of Localized
Page 11 and 12: RDNLS: a straightforward proof of e
Page 13 and 14: Anderson Representation of DNLS nor
Page 15: Quasiperiodic Periodic Solutions: B
Page 18 and 19: The probability to find an initial
Page 20 and 21: Assume the wavepacket spreads unifo
Page 22 and 23: Example: What is the behavior of a
Page 24 and 25: V Diffusion of a Wavepacket in nonl
Page 26 and 27: There are initial conditions with n
Page 28 and 29: VI-New Numerical Investigations G.
Page 30 and 31: Serge Aubry, Aubry, LLB, FRANCE t=1
Page 32 and 33: Participation number of norm distri
Page 34 and 35: Serge Aubry, Aubry, LLB, FRANCE Tim
Page 36 and 37: Scenario for the Absence of spreadi
Page 38 and 39: Warning about the problem of reliab
Page 40 and 41: VII Summary and concluding remarks

Serge Aubry - Physics Department . Technion

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