Scattering of small-amplitude phonons on discrete breathers in Fermi-Pasta-Ulam-Tsingou chain

Abstract

There are two traditionally discussed dispersion relations (DR) in condensed media: gapless phonon DR and DR with an energy or frequency gap. The third type of DR is of interest in various fields of condensed matter physics: states corresponding to gap effects in k-space (Gapped Momentum States - GMS). The growing interest in GMS is associated with important consequences for the dynamic and thermodynamic properties of the system (hydrodynamic turbulence, plasticity, fracture). Traditionally, GMS arise in the Maxwell-Frenkel approach as applied to the viscoelastic properties of liquids and solids, when the DR-gaps can continuously vary from energy to momentum space. This work is the first in a series of studies devoted to the analysis of dispersion effects associated with the anharmonicity of the potential and the emergence of collective breather-type modes, the so-called discrete breathers (DBs), and their influence on the macroscopic properties of nonlinear lattices, for example, on the heat conductivity. Recently, the influence of discrete breathers (DBs) on the macroscopic properties of nonlinear lattices, for example, on thermal conductivity has been investigated. When solving this problem, it is important to know how phonons interact with DBs. The scattering of phonon wave packets of small amplitude by standing DBs in the β-Fermi-Pasta-Ulam-Tsingou (β-FPUT) chain is studied numerically for different amplitudes of DBs. It is found that DBs of sufficiently large amplitudes reflect short-wavelength phonons, but remain transparent for long-wavelength phonons. An increase in the DB amplitude expands the reflection region in the short-wavelength part of the first Brillouin zone. These results suggest that DBs in the β-FPUT chain do not strongly affect the thermal conductivity, since heat is transferred mainly by long-wavelength phonons, which are weakly affected by DBs.