Dielectric response spectrum of a damped one-dimensional double-well oscillator

The characteristic features of the dielectric response spectrum associated with the condensation of a ‘‘soft’’ phonon mode during a ferroelectric phase transition can be reproduced by an oscillator moving in a damped linear double-well potential. The behavior of the response function below the transition temperature $T_c$ can be simulated by introducing a linear mean-field coupling which destroys the symmetry of the well. Potentials derived from physically realistic parameters are shown to result in dielectric responses which are in order-of-magnitude agreement with experimental values.