Markovian property of cooperative fluctuations investigated by light scattering spectroscopy

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We have Ivestigated the Stokes to anti-Stokes intensity ratio for the low-frequency light scattering spectra of a paraelectric potassium dihydrogen phosphate (KDP) crystal. The usual relation determined by the Boltzmann factor holds at 293K. However the relation is not satisfied for the soft mode occurring for ω<30 cm-1 near the phase transition temperature, and the intensity ratio relative to the Boltzmann factor is about 0.94 at ω=15cm-1. The Markovian nature of the soft mode that introduces time-irreversibility may be essential for understanding the behavior of the mode like a classical fluctuation. Further investigation on the temperature dependence is needed for clarifying the evolution of the soft mode from microscopic quantum motions to the classical and macroscopic dynamics as temperature approaches Tc.We compare the present result of the soft mode with that of the cooperative rotational dynamics in liquid. In liquid carbon disulfide CS2, the intensity of Im(ω) changes with temperature below 50 cm-1. On the other hand, the deviation of the intensity ratio from the Boltzmann factor is observed only for ω<5cm-1 at 292K. This frequency region is much narrower than that where Im(ω) varies with temperature. The result is in contrast to the case of KDP where the deviation is observed almost in the same region where Im(ω) appreciably changes with temperature. This implies that although both the dynamics are dissipative, the degree of dissipation causing the Markovian nature of the soft mode is higher than that for the cooperative rotational dynamics. This may be related to the macroscopic character of the soft mode near Tc as a critical fluctuation.