  We present a simple and microscopic physical model that breaks the
ergodicity. Our model consists of coupled classical harmonic oscillators, and
the motion of the tagged particle obeys the generalized Langevin equation
satisfying the second fluctuation dissipation theorem. It is found that
although the nonergodicity strength, which is expected to detect the ergodicity
breaking, for this model vanishes, the velocity auto correlation function of
the tagged particle asymptotically oscillates. We analyze the model by using
the molecular dynamics and the exact diagonalization as well as the rigorous
mapping to the generalized Langevin equation. Our analysis reveals that the
asymptotic oscillation is caused by a localized mode with an isolated frequency
from the continuous phonon spectrum.
