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


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.