Effect of discrete breathers on macroscopic properties of the Fermi-Pasta-Ulam chain

Abstract

For a number of crystals the existence of spatially localized nonlinear vibrational modes, called discrete breathers (DBs), has been demonstrated using molecular dynamics and in a few cases the first-principle simulations. High-resolution imaging of DBs is a challenging task due to their relatively short lifetime ranging typically from 10 to 10 3 atomic oscillation periods (1 to 100 ps). Another way to prove that DBs exist consists in evaluation of their effect on macroscopic properties of crystals. In this paper, we study the effect of DBs on macroscopic properties of the Fermi-Pasta-Ulam chain with symmetric and asymmetric potentials. The specific heat, thermal expansion (stress), and Young's modulus are monitored during the development of modulational instability of the zone boundary mode. The instability results in the formation of chaotic DBs followed by the transition to thermal equilibrium when DBs disappear due to energy radiation in the form of small-amplitude phonons. Time evolution of the macroscopic properties during this transition is monitored. It is found that DBs reduce the specific heat for all the considered chain parameters. They increase the thermal expansion when the potential is asymmetric and, as expected, thermal expansion is not observed in the case of symmetric potential. The Young's modulus in the presence of DBs is smaller than in thermal equilibrium for the symmetric potential and for the potential with a small asymmetry, but it is larger than in thermal equilibrium for the potential with greater asymmetry.