Discrete breezers in a three-dimensional lattice with a Fermi-Pasta-Ulam-Zingou potential

The paper considers such nonlinear phenomena in condensed matter physics as Discrete Breezers (DB) and delocalised nonlinear vibrational modes (DNVM). DB are spatially localised vibrational modes of large amplitude that exist under conditions of nonlinearity of interatomic interactions and discreteness of the medium. The oscillation frequency of DB lies outside the phonon spectrum of low-amplitude crystal vibrations and does not resonate with phonons, i.e. it does not waste its energy on their excitation. DNVM are vibrational modes manifested in crystal lattices with translational symmetry, which exist for any oscillation amplitudes and regardless of the type of interaction between the elements of the system. In early works, the authors established a connection between DB and DNVM. A three-dimensional Body Centered Cubic (BCC) lattice with nearest and next-nearest interactions described by the β-Fermi-Pasta-Ulam-Tsingou (FPUT) interatomic potential is investigated. Properties of DNVM with the wave-vector on the boundary of the first Brillouin zone are analysed. DNVM are exact solutions to the equations of motion that can be found from the analysis of only the symmetry of the bcc lattice. Frequency response of DNVM for the case of soft- and hard-type anharmonicity is calculated. In the case of hard-type anharmonicity, four DNVM have frequencies bifurcating from the upper edge of the phonon spectrum and growing with the amplitude. By superimposing localisation functions on these DNVM, various DB were obtained, which were attributed to quasi-breezers. They are not single-frequency oscillatory modes with a finite lifetime and are formed due to overcoming the strength of the intersite potential. As a result of the study, six long-lived quasi-freezers were obtained based on four DNVM frequencies above the phonon band. The results of this study confirm the effectiveness of the search for long-lived quasi-freezers in complex lattices, starting with the analysis of DNVM. In the future, the obtained quasi-breeze solutions can be used as initial conditions for an iterative procedure for searching for exact DB. Thus, the presented work demonstrates a practical approach to the search for DB in high-dimensional lattices.

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