Inherent Effects of Discretization in an Interacting Kink-Phonon System

Abstract

There is a considerable body of knowledge about classical 1-D systems capable of supporting nonlinear soliton-like excitations [l]. We know, for example, that the free energy of a discretized Sine-Gordon (SG) or Φ⁴ chain exhibits parts which may be directly related to independent “gases” of linear (phonon) and nonlinear (kink) modes respectively [2]. Linear stability analysis [3] tells us that kinks are transparent to small oscillations of the underlying continuum; interactions can be characterized, to first order, by a phase shift, which in turn reduces the density of states available to linear modes, to allow for the kink degrees of freedom. This energy sharing, when taken into account, improves the agreement between configurational phenomenology and exact (transfer integral) results [4]. We can even go one step further and examine second order effects, to conclude that solitons perform a diffusive motion under the influence of thermal phonons yet no energy is being exchanged between nonlinear and continuum linear modes [5].