Serge Aubry - Physics Department . Technion
Serge Aubry - Physics Department . Technion Serge Aubry - Physics Department . Technion
There are initial conditions with no diffusion at all For example: Intraband discrete breathers Almost no diffusion (?) for small amplitude initial wavepacket or close to anticontinuous limit Quasiperiodic solutions? There are initial conditions with apparently initially strong diffusion (with strong chaos Shepelyansky) The most studied!!! Serge Aubry, Aubry, LLB, FRANCE
Conjectures for Infinite Nonlinear Arrays with linear Anderson Localization (purely discrete spectrum with no mobility threshold) There are two kinds of Initial Conditions which both may be obtained both with finite probability 1- Solutions which are purely quasiperiodic from the begining (infinite dimension invariant tori). Their probability goes to 1 at small norm or close to the anticontinuous limit or close linearly stable IDB solutions. 2-Solutions which are initially Chaotic but slowly converge to a quasiperiodic profile. Self-organization profile. Initial resonances are spontaneously removed by energy radiation through non excited Anderson modes which may generate a long tail. No Diffusion at all for any initial l 2 wave packet. 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 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
Conjectures for Infinite Nonlinear Arrays with linear Anderson<br />
Localization (purely discrete spectrum with no mobility threshold)<br />
There are two kinds of Initial Conditions which both may be obtained<br />
both with finite probability<br />
1- Solutions which are purely quasiperiodic from the begining (infinite<br />
dimension invariant tori). Their probability goes to 1 at small norm<br />
or close to the anticontinuous limit or close linearly stable IDB<br />
solutions.<br />
2-Solutions which are initially Chaotic but slowly converge to a<br />
quasiperiodic profile. Self-organization profile.<br />
Initial resonances are spontaneously removed by energy radiation<br />
through non excited Anderson modes which may generate a long tail.<br />
No Diffusion at all for any initial l 2 wave packet.<br />
<strong>Serge</strong> <strong>Aubry</strong>, <strong>Aubry</strong>,<br />
LLB, FRANCE
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