Serge Aubry - Physics Department . Technion
Serge Aubry - Physics Department . Technion Serge Aubry - Physics Department . Technion
Examples: Klein-Gordon systems 1,2 or 3D (anharmonic oscillators coupled by harmonic springs FPU systems (with gapless accoustic phonons) Serge Aubry, Aubry, LLB, FRANCE nonlinear springs The system at infinity behaves like linear and generate an effective frequency dependant damping on the dynamics Filtering the resonant components (Consequence:no damping for Discrete Breathers) Discrete Breathers may be dynamical ATTRACTORS in INFINITE Hamiltonian systems
Initial wavepacket Time periodic solution Initial Spontaneous Formation of a DISCRETE BREATHER no radiation Limit Serge Aubry, Aubry, LLB, FRANCE Sievers and Takeno (1988): from a initial localized wavepacket radiation Chaotic or « quasiperiodic » transient Transient radiation A large part of the initial energy remains localized as a DB, the rest spreads to zero at infinity The second moment diverges but the participation number does not
- Page 1 and 2: Suppression of Energy Diffusion in
- Page 3: I-Nonlinear spatially periodic syst
- 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
Examples: Klein-Gordon systems 1,2 or 3D<br />
(anharmonic oscillators coupled by harmonic springs<br />
FPU systems (with gapless accoustic phonons)<br />
<strong>Serge</strong> <strong>Aubry</strong>, <strong>Aubry</strong>,<br />
LLB, FRANCE<br />
nonlinear springs<br />
The system at infinity behaves like linear and generate<br />
an effective frequency dependant damping on the dynamics<br />
Filtering the resonant components<br />
(Consequence:no damping for Discrete Breathers)<br />
Discrete Breathers may be dynamical ATTRACTORS<br />
in INFINITE Hamiltonian systems
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