Anharmonic Chain with Lennard-Jones Interaction

Abstract

The classical equations of motion of a one-dimensional, finite, anharmonic lattice, with nearest-neighbor interaction of the Lennard-Jones type, are investigated numerically. The results indicate that when the vibrational energy per particle is equal to or greater than 2-3% of the depth of the potential well, one has, in time average, equipartition of the energy among the normal modes, thus giving a hint toward ergodicity of the system at sufficiently high energy. For lower energies one finds recurrent motions if initially only one normal mode is excited in analogy with a famous result due to Fermi, Pasta, and Ulam. In this case the numerical results are consistent both with the existence of a long relaxation time and with a lack of ergodicity for low energies.