A unified approach to the interpretation of displacive and order–disorder systems. II. Displacive systems

Abstract

In the displacive limit of a one-dimensional coupled double-well model, three sets of propagating solutions of the corresponding nonlinear field equation are exhibited. It is shown that knowledge of their amplitude and their energy suffices to interpret the variation with the temperature and the wave vector of the numerically calculated three-peaks structure of the dynamical correlation function. In addition, Lorentz invariance of the nonlinear field equation shows that localized solutions (propagating walls) have the properties of a relativistic particle, the limit velocity of which is a sound velocity. These propagating walls exhibit nontrivial interactions and, therefore, do not have the usual soliton properties. The behavior of the central peak and specifically the nonzero frequency of the latter, for a nonzero wave vector, is explained by assuming a perfect relativistic gas of such moving walls.