Dynamics of non-linear monatomic and diatomic chains at a T=0 first-order phase transition point

Abstract

One-dimensional monatomic and diatomic chains with harmonic coupling between neighbouring sites and an on-site anharmonic potential V( phi )=C phi 2n+2+B phi n+2+A phi 2+D are examined in the displacive limit, which serves as a model for a structural phase transition. Kink solutions are obtained at the T=0 first-order phase transition point for B2=4AC, A, C>0, B<0 and D=0 for arbitrary values of n. Non-linear periodic solutions (non-linear phonons) are obtained for n=1, and these are also found to be the solutions of discrete equations of motion. The solutions are shown to be stable and have finite energy.