Anharmonic oscillator model for first order structural phase transition

Exact solutions for the motion of a classical anharmonic oscillator in the potentialV(φ)=Bφ ² ? |A|φ ⁴ +Cφ ⁶ are obtained in (1 + 1) dimensions. Instanton-like solutions in (imaginary time) which takes the particle from one maximum of the potential to the other are obtained in addition to the usual oscillatory solutions. The energy dependence of the frequencies of oscillation is discussed in detail. This can be used as a model for the first order structural phase transition in the mean field approximation. The high and low temperature behaviour of the static susceptibility is obtained. Finally, a qualitative explanation is offered for the observed central peak in ferroelectrics like SrTiO₂.