Serge Aubry - Physics Department . Technion

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

Example: What is the behavior of a wavepacket if no spreading to zero is possible. (periodic case: independant of n: generation of mobile Discrete Breathers (« Discrete Compactons ») which radiates wavelets and stops (numerically observed for periodic systems by S. Flach) Consequence: The limit profile is quasiperiodic. Random case: Same conjecture Serge Aubry, Aubry, LLB, FRANCE
In the Anderson base same model, the random DNLS Model belong to this family of NONdiffusive Hamiltonian except that operator L (though it is diagonal), is not proportional to unity but is random. Why extra randomness would generate diffusion? Conjecture: for RDNLS, the limit profile of any initially localized wavepacket should be or become quasiperiodic (as an infinite dimension invariant torus). Serge Aubry, Aubry, LLB, FRANCE
Page 1 and 2: Suppression of Energy Diffusion in
Page 3 and 4: I-Nonlinear spatially periodic syst
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 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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