# Graduate School in Nonlinear Science

### Sponsored by the Danish Research Academy

**
MIDIT OFD CATS
Modelling, Nonlinear Dynamics Optics and Fluid Dynamics Chaos and Turbulence Studies
and Irreversible Thermodynamics Risø National Laboratory Niels Bohr Institute and
Technical University of Denmark Building 128 Department of Chemistry
Building 321 P.O. Box 49 University of Copenhagen
DK-2800 Lyngby DK-4000 Roskilde DK-2100 Copenhagen Ø
Denmark Denmark Denmark
**

**DISCRETE BREATHERS IN APERIODICALLY ORDERED DIATOMIC FPU LATTICES **

by **Erik Lennholm**

Department of Physics and Measurement Technology, University of Linkoping,
Sweden

Thursday November 4, 1999, 15:00 h

MIDIT, IMM, Bldg. 305, Room 027, DTU

MIDIT Seminar 470

**Abstract**:
The concept of discrete breathers, i.e., intrinsically localized
modes, has during the last decade become a field which has gained
much interest from various branches of physics, e.g., biophysics
and solid state theory. The basic idea is that an added nonlinear
term to the equations gives rise to localized modes in the normally
forbidden frequency range of the linear models. This prevents the
excitation of propagating phonon modes which could carry away the
breather energy and destroying it.

We investigate the existence of breathers in aperiodically
ordered diatomic lattices, namely the Fibonacci and Thue-Morse
lattices. The dispersion relation (phonon spectrum) for an
aperiodic lattice with long range order contains generally a dense
set of gaps. This makes it a natural question to pose whether
discrete breathers exist also in these kinds of systems and if the
gaps in the dispersion relation make the non-resonance condition
easier to fulfil?

Starting from the limit of excitations of one isolated
light atom we obtain discrete breather solutions. The found exact
solutions are used, slightly perturbed, as initial conditions for
long-time simulations of the breathers. These breathers turn out
to be robust. Finally we consider how initial excitations of two
consecutive light atoms evolve. Depending on the properties of the
phase space for the two-atom system, we obtain different
behaviour of these excitations. Especially we find that the
aperiodic lattices can support localized excitations with a
continuous frequency distribution for the time-scales we consider,
while a periodic lattice is unable to.