Soft mode dynamics and spatio-temporal symmetry breaking in a thermo-convective system

Abstract

Using neutron scattering we have studied the behaviour of an oscillatory soft mode in a thermoconvective liquid crystal. As a function of an applied vertical temperature difference ΔT the behaviour of the soft-mode frequency defines four regimes, separated by cross-over values at which spatio-temporal symmetry is broken. Breaking of time symmetry manifests itself in different phase relations among localized oscillators. Incomplete softening at the convection threshold ΔTc is interpreted as anharmonic coupling to low-energy, internal director fluctuations in the nematic. Subtracting the anharmonic contribution, the renormalized frequency squared gives a susceptibility critical index γ for each of the four regimes. The values range between 1.1 and 2.7, indicative of a change of the spatial dimensionality as ΔT→ΔTc. The widths in ΔT of the regimes converge as the Feigenbaum ratio (∼4.6), and the meaning of this is discussed.