Discrete nonlinear Schrödinger breathers in a phonon bath
Theoretical Division and Center for Nonlinear Studies, Los Alamos National
Laboratory, Los Alamos, New Mexico 87545, USA
Revised: 20 September 1999
Published online: 15 May 2000
We study the dynamics of the discrete nonlinear Schrödinger lattice initialized such that a very long transitory period of time in which standard Boltzmann statistics is insufficient is reached. Our study of the nonlinear system locked in this non-Gibbsian state focuses on the dynamics of discrete breathers (also called intrinsic localized modes). It is found that part of the energy spontaneously condenses into several discrete breathers. Although these discrete breathers are extremely long lived, their total number is found to decrease as the evolution progresses. Even though the total number of discrete breathers decreases we report the surprising observation that the energy content in the discrete breather population increases. We interpret these observations in the perspective of discrete breather creation and annihilation and find that the death of a discrete breather cause effective energy transfer to a spatially nearby discrete breather. It is found that the concepts of a multi-frequency discrete breather and of internal modes is crucial for this process. Finally, we find that the existence of a discrete breather tends to soften the lattice in its immediate neighborhood, resulting in high amplitude thermal fluctuation close to an existing discrete breather. This in turn nucleates discrete breather creation close to a already existing discrete breather.
PACS: 63.70.+h – Statistical mechanics of lattice vibrations and displacive phase transitions / 63.20.Pw – Localized modes / 63.20.Ry – Anharmonic lattice modes
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 2000