Slow energy relaxation in anharmonic chains with and without on-site potentials: Roles of distinct types of discrete breathers

Abstract

Slow energy relaxation has been observed in one-dimensional lattices with and without a nonlinear on-site potential; however, a comprehensive understanding of the detailed relaxation process remains elusive. Here we revisit this issue by introducing damping conditions at the free-end boundary of a thermalized lattice. We reveal that, in the long-cooling-time regime considered, for systems with a nonlinear on-site potential, energy relaxation exhibits a strong temperature-dependent behavior and with the increase of temperature, there is a crossover between decaying and non-decaying behaviors, around a crossover temperature point of Tc≃4.2. This non-decaying behavior at higher temperature is attributed to the presence of standing multi Sievers–Takeno discrete breather (DB) states. Conversely, for systems without on-site potentials, relaxation is nearly independent of temperature but dependent on interparticle potential. Notably, we observe that the cubic anharmonicity can generate moving single Page DB states that contribute to the unusual slow energy relaxation within a specific time regime. Our results provide enhanced insights into the mechanisms governing slow energy relaxation during lattice cooling.