Serge Aubry - Physics Department . Technion

More documents

Recommendations

Info

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

Serge Aubry, Aubry, LLB, FRANCE Time Fourier transform of the participation number The limit profile tends to be quasiperiodic! Same result for the time Fourier transform at a single central site
Numerical arguments for KAM tori as limit profile of an initially localized wavepacket 1-The participation ratio of the energy distribution does not diverge. 2- The amplitude of the at any site does not decay to zero though it oscillates indefinetely. 3-The largest Lyapounov exponent initially drops by 2 or 3 orders of magnitude while the wavepacket does not spread to small amplitude. It continues to decay but slower and slower. 4- Simultaneously, the Fourier spectrum of the atomic motion near center from broad band becomes narrow band with thin line widths Conclusion: The attractor of the system (limit profile) might be a KAM tori ? but very slow convergence (Arnol’d diffusion?) What about the evolution for times beyond those numerically available? Need a mathematical proof? 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 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 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

You also want an ePaper? Increase the reach of your titles

Delete template?

Save as template?