The thermodynamic parameters of phonon-soliton equilibrium in one-dimensional Frenkel-Kontorova systems

The temperature dependences of the internal energy of a canonical ensemble of Frenkel-Kontorova systems, which are one-dimensional chains of material points linked by elastic bonds in a periodic potential, were studied by the Monte Carlo method with importance sampling. Such a model is an example of a system in which local contraction-extension states that can move as sole waves, solitons, are possible. The calculation results are analyzed on the basis of the model of an equilibrium reaction between a chain phonon and soliton that occurs at the given temperature. The model was used to estimate the thermodynamic parameters of phonon-soliton equilibrium and obtain the dependences of the enthalpy of equilibrium “reaction” on the incommensurability parameter of the chain γ. The enthalpy of this process was found to be described by a linear dependence on γ−1/2 with a high correlation degree (r 2 = 0.994).