DISSIPATIVE DYNAMICS OF THE FRENKEL-KONTOROVA MODEL

The aim of this review article is to present recent advances in the th eory of the dynamics of modulated phases in the Frenkel-Kontorova mode l. This theory is motivated through two specific condensed matter syst ems: charge-density wave conductors and Josephson junction arrays. The presentation tries to integrate the existing results into the perspec tive of the equilibrium theory of the model, which is summarized in th e beginning. The issues of defectibility, metastability, pinning and s ynchronization are discussed in connection with the underlying interpl ay of continuum and discrete descriptions. Special emphasis is placed on the different transitions between dynamical phases; namely depinnin g transition, unlocking transition and dynamical Aubry transition.