Spontaneous Polarization of a Gas of Two-Level Molecules and the Gibbs Quasi-Energy Distribution

We study the possibility of spontaneous formation of a polarization structure in a thermodynamically equilibrium gas of dipolarly interacting two-level molecules. Using the Maxwell-Bloch equations within the framework of the mean-field theory, we find that the antiferroelectric phase transition in a gas with a weak relaxation of the polarization is always a second-order transition. It is shown that if relaxation is neglected, then in the quasi-classical consideration of the translational motion of molecules in the polarization wave, the energy levels of a separate molecule coincide with its quasi-energies that are well known in quantum optics. Thus, to study the statistical properties of the antiferroelectric phase, we apply the generalized Gibbs distribution over quasi-energy states of the molecules. As a result, we determine the characteristic features and the possible parameters of the antiferroelectric state of a gas. In particular, it is found that, owing to the Doppler resonance of part of the molecules with the polarization wave, the properties of the gas antiferroelectrics behind the phase-transition point may radically differ from the properties of the conventional ferroelectrics in the Ginzburg-Landau theory. We also analyze the influence of polarization fluctuations for the case of a ferroelectric transition in a gas.