Serge Aubry - Physics Department . Technion
Serge Aubry - Physics Department . Technion
Serge Aubry - Physics Department . Technion
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II- Exact Time Periodic Solutions (Intraband Discrete Breathers)<br />
in Random and Nonlinear Systems<br />
(with linear Anderson lOCALIZATION)<br />
Kopidakis <strong>Aubry</strong> 1999-2000<br />
Random systems: When the linear spectrum is discrete.<br />
(Anderson localization) no linear phonon radiation is possible<br />
Existence Proofs of Intraband DBs (IDBs)<br />
Theorem: Albanèse and Frohlich 1991<br />
Anderson modes persist in nonlinear models as time periodic<br />
solutions with frequencies in a fat Cantor set.<br />
Numerical Calculations (at computer accuracy) of intraband<br />
Discrete Breathers : KA 1999-2000<br />
1- Quasi-continuation in L 2 : Each Anderson mode generates a family<br />
of IDBs with frequency in a FAT CANTOR SET (with nonvanishing measure)<br />
2- Continuation in L ∞ : Each Anderson mode becomes an extended multiDB<br />
with infinite energy<br />
<strong>Serge</strong> <strong>Aubry</strong>, <strong>Aubry</strong>,<br />
LLB, FRANCE
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