Mechanisms of motion of vibrational solitons

Abstract: Previous studies of nonlinear dynamics have shown that local vibrational excitations, both stationary and moving, can exist in ideal anharmonic atomic lattices [1,2]. These excitations are called vibrational solitons, intrinsic localized modes, or discrete breathers (DBs). Large-size low-frequency DBs in atomic chains have high mobility. However, when the size of the DB is small, the discreteness of the atomic lattice breaks the continuous symmetry and leads to the capture of the moving DB by the Peierls-Nabarro potential barrier. Nevertheless, as we have shown [3,4], DBs in metals Fe, Cu, Ni, Nb and in some other crystals can move on a long distance. DBs are most likely responsible for the transmission of signals in biological chains. We investigated in detail the mobility of DBs in the Fermi, Pasta and Ulam lattice (FPU) and found that the odd (cubic (k_3) and fifth (k_5)) anharmonicity strongly promotes the mobility of DB. We also found that the mobility of BDs strongly depends on the linear localized modes (LLMs) previously predicted by us [6] – the phonons captured by DB: these modes promote the interaction of DBs with phonon continuum. Moreover, we found that initially stationary or captured after moving a DB of the high or medium frequency range is sooner or later converted into a DB of medium frequency with a long service life, propagating along the chain over a long distance without capture. The process begins with an increase in the amplitude of vibrations of the energy centers DB in time; the movement begins when this amplitude reaches half the distance between the atoms. And in this case, odd anharmonicity is also an important factor – it greatly contributes to the mobility of DBs. The amplification of the vibrations of the energy center and the subsequent movement occur due to the radiation of low frequency phonons with a momentum. This radiation is the result of the common nonlinear action of DB and LLM. Thus, a moving DB in the lattice is like a rocket: it emits particles (here low-frequency phonons) with a pulse in the opposite direction, which makes it possible to overcome the braking caused by radiation processes. We also found that a well-chosen fifth anharmonicity leads to the disappearance of the Peierls-Nabarro barrier and to an inversion of stability between bond-centered and site-centered DBs, and, in fact, to essentially non-radiative propagation of a DB along the chain.

1. A.J. Sievers, S. Takeno, Phys. Rev. Lett. 61, 970 (1988). 2. S. Flach and C. R. Willis, Phys. Repts. 295, 181 (1998). 3. M. Haas, V. Hizhnyakov, A. Shelkan, M. Klopov, and A. J. Sievers, Phys. Rev. B 84, 144303 (2011). 4. V. Hizhnyakov, M. Haas; A. Shelkan, M. Klopov, Physica Scripta, 89 (4) (2014). 5. A. Shelkan, M. Klopov, V. Hizhnyakov, Phys. Lett. A 383, 1893 (2019). 6. V. Hizhnyakov, A. Shelkan, M. Klopov, S.A. Kiselev, A.J. Sievers, Phys. Rev. B 73, 224302 (2006).

astrophysicscondensed mattergeneral relativity and quantum cosmologyhigh energy physicsmathematical physicsclassical physicsgeneral physics

Audience: researchers in the topic

Theoretical physics seminar @ Tartu