Power spectrum density in a paraelectric particle in zero-frequency limit

Abstract

In this paper, we study the behavior of the particle in the paraelectric phase near the bulk critical temperature (a = 0) (in our units) and near the particle critical temperature (ad) using the fluctuation–dissipation theorem through the power spectrum density S(ω) at zero frequency ω = 0 in the particle. This power spectrum density is found here to have three regimes as concerning the temperature dependence for a given particle diameter. The first one is above the bulk critical temperature, the second one is at the bulk critical temperature and the third is below the bulk critical temperature and above the particle critical temperature. Decreasing temperature fluctuations of the order parameter (polarization) change from the bulk-like to the particle-like due to particle form. Divergency of the bulk spectrum density Sb(0) at the bulk critical temperature a = 0 is compensated in the particle by the contribution ≈a2due to the particle form. The power spectrum density S(0) near the particle critical temperature diverges with the exponent 2, we obtain [Formula: see text], where Tc, dis the particle critical temperature in the temperature variable T. Our results are new and are exact within the model used.