Serge Aubry - Physics Department . Technion

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

Existence proofs od Discrete Breathers (spatially localized Time periodic solutions) Existence Proofs of DBs in many nonlinear models 1- by the Principle of Anticontinuity (MacKay SA 1994 Klein-Gordon 2- Bambusi 1996 3- Livi Mackay Spicci 1997 dimer FPU 4- SA 1998 5- SA, Kopidakis and Kadelburg 2001 (Variational) Arioli Gazola 6- G. James 2003 Serge Aubry, Aubry, LLB, FRANCE
II- Exact Time Periodic Solutions (Intraband Discrete Breathers) in Random and Nonlinear Systems (with linear Anderson lOCALIZATION) Kopidakis Aubry 1999-2000 Random systems: When the linear spectrum is discrete. (Anderson localization) no linear phonon radiation is possible Existence Proofs of Intraband DBs (IDBs) Theorem: Albanèse and Frohlich 1991 Anderson modes persist in nonlinear models as time periodic solutions with frequencies in a fat Cantor set. Numerical Calculations (at computer accuracy) of intraband Discrete Breathers : KA 1999-2000 1- Quasi-continuation in L 2 : Each Anderson mode generates a family of IDBs with frequency in a FAT CANTOR SET (with nonvanishing measure) 2- Continuation in L ∞ : Each Anderson mode becomes an extended multiDB with infinite energy 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: Initial wavepacket Time periodic so
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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