Quantum dynamics in the highly discrete, commensurate Frenkel Kontorova model: A path-integral molecular dynamics study

Abstract

The commensurate Frenkel Kontorova (FK) model is studied using path-integral molecular dynamics (PIMD). We focus on the highly discrete case, in which the embedding potential has a much greater maximum curvature than the harmonic potential connecting two particles in the FK chain. When efficient sampling methods are used, the dynamical interpretation of adiabatic PIMD appears to represent quite accurately the true time correlation functions of this highly correlated many-body system. We have found that the discrete, quantum FK model shows different behavior than its continuum version. The spectral density does not show the characteristic omega-2Theta(omega-omegac) cusp of the continuum solution in the pinned phase (m>m(c)). We also identify a dynamical quantum hysteresis in addition to the regular classical hysteresis when an external force is applied to the FK chain. In the unpinned phase (m<or=m(c)), we find a linear response damping coefficient which is finite and only weakly dependent on temperature T at small values of T.