Anomalous Thermostat and Intraband Discrete Breathers
S.Aubry, R. Schilling

TL;DR
This paper studies the dynamics of anharmonic systems embedded in harmonic lattices, revealing conditions for energy transfer, dissipation, and the existence of non-relaxing intraband discrete breathers across a range of frequencies.
Contribution
It proves the existence of intraband discrete breathers for all frequencies in a Cantor set with finite measure, and analyzes energy transfer and dissipation properties in such systems.
Findings
Energy transfer rate varies with frequency, being quadratic at phonon frequencies.
Harmonic bath can act as an anomalous thermostat with non-standard dissipation.
Intraband discrete breathers exist for a set of frequencies with positive measure.
Abstract
We investigate the dynamics of a macroscopic system which consists of an anharmonic subsystem embedded in an arbitrary harmonic lattice, including quenched disorder. Elimination of the harmonic degrees of freedom leads to a nonlinear Langevin equation for the anharmonic coordinates. For zero temperature, we prove that the support of the Fourier transform of the memory kernel and of the time averaged velocity-velocity correlations functions of the anharmonic system can not overlap. As a consequence, the asymptotic solutions can be constant, periodic,quasiperiodic or almost periodic, and possibly weakly chaotic. For a sinusoidal trajectory with frequency we find that the energy transferred to the harmonic system up to time is proportional to . If equals one of the phonon frequencies , it is . We prove that there is a full…
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